Do Protestants accept the similarity between Mary and the Ark of the Covenant?

OP

The Ark of the Covenant was overshadowed (Ex. 40:34-35)

Mary was overshadowed by the Holy Spirit (Lk. 1:35)

Not exactly. If we look at what scripture says, we find that the tabernacle was overshadowed, though the ark was inside. The ark per se, alone, was not singled out as overshadowed.

Moses had set the ark in the inner room, in the Holy of Holies within the inner veil of the tabernacle of Moses (Exo 40:21).

Once completed, of age if you will, the whole tent was overshadowed.

Then a cloud covered the tent of the congregation, and the glory of the LORD filled the tabernacle. Exo 40:34

In other words, the type is more a picture of Mary as the tent of what's inside. She was "overshadowed", as the whole tabernacle was, but the point is the ark is inside; that is, with Christ the Ark within. Mary thus "overshadowed" gives birth to the Ark, rather than the ark being Mary.

OP

David was rejoicing in the presence of the Ark of the Covenant (2 Sam. 6:16)

John the Baptist leaped for joy in the presence of Mary (Lk. 1:41)

Again not really. Elizabeth's baby is not leaping for joy in the presence of Mary, but rather because of the fruit of Mary's womb; that is, Jesus Christ.

And it came to pass, that, when Elisabeth heard the salutation of Mary, the babe leaped in her womb; and Elisabeth was filled with the Holy Ghost: And she spake out with a loud voice, and said, Blessed art thou among women, and blessed is the fruit of thy womb. And whence is this to me, that the mother of my Lord should come to me? For, lo, as soon as the voice of thy salutation sounded in mine ears, the babe leaped in my womb for joy. Luk 1:41-44

The joy comes from recognizing the Ark within the tent (the carrier Mary).

OP

David said, Why did the Ark of the Lord visit me? (2 Sam. 6:9)

Elizabeth said, Why did the mother of the Lord visit me?( Lk. 1:43)

Like with the other two "examples" trying to force an interpretation that does not exist, so too is this comment divorced from Scripture and context.

And David was afraid of the LORD that day, and said, How shall the ark of the LORD come to me? 2 Sam 6:9

David is afraid. He has no idea how to move the ark. His jealousy of the blessing, however, overshadows his fear. He leads the ark back to Jerusalem with sacrifices of oxen every 6 paces. There's no sense of comparison as Elizabeth is happy to see Mary. There's no sense of fear or envy at that stage.

So, while it is apparent that Mary may be compared to the tent that held the ark, the ark itself is a type of Christ.

I think it is an overstatement to say that the word is only used by Mary and the Ark in the entire Scripture.

The same verb is used in the accounts of the transfiguration (Matt. 17:5; Mark 9:7; Luke 9:34). Kittel in, Theological Dictionary of the New Testament, did mentioned:

The literal meaning “to overshadow,” “to cast a shadow,” occurs in Act 5:15. In the background is the popular view of the apostle Peter as the person who heals all sickness.

In the Old Testament, it also occurs in Deuteronomy 11:12, Psalms 91:4 and Isaiah 32:14-17.

The parallelism for David's fear of the Ark versus Elizabeth's joy in acknowledging the divinity of the child seem stretch.

Also, the Greek word, skirtao, tends to be associated with "the movements of the child in the womb" and "these movements express joy, jubilation". Kittel mentions:

Two motifs control the use in Luke: the natural movement of the child in the womb, and eschatological joy at the coming of Christ. The former is prefigured in Gen 25:22 the latter in Mal 4:2, where the comparison gives expression to joy at eschatological salvation.

Both are the Hebrew equivalent of the Greek Word, skirtao.

If I will be generous, it is the proximity of Mary next to Jesus, as the reality of the type of the Ark of the Covenant, that these passages seems "similiar".

EDIT: It would seem that I will now hold the assumption that the exact conjugation holds.

If so, there must be consistency of the interpretation of the types. A type (Gk. typos, from typtö, “to strike”) is a stamp, pattern, or mold, indicating that a pattern or idea is applied to someone or something else. The analogy of a typeface in printing and its corresponding image is helpful.

Types may be persons (Adam), offices (the priesthood and kingship), entities (the tabernacle), or events (the Passover and Israel’s wandering in the wilderness).

Traditionally, David is a type of Christ and to associate it with John the Baptist is stretching it. And again, the same argument holds to David as a type of Elizabeth.

With this, I would not be surprised if most writers outside of Catholicism have even consider the similarity (in my humble opinion) when the types of Christ is more outstanding and consistent.

Below are some of the writers:

Benjamin Keach (1640-1704), a Baptist, wrote in his book, "Preaching TYpes & Metaphors):

THE ARK A TYPE OF CHRIST The Ark was an assurance of God's presence amongst his people : so Christ is the cause and assurance, that God in a gracious way is present with us. Where the Ark was, there it was lawful to offer sacrifice, and no where else: which might show that our acceptance in God's sight, is through Jesus Christ.

Kenneth E. Trent, in his book, "Types of Christ in the Old Testament", quoted:

The ark is one of the most dramatic and outstanding types of Christ found anywhere in the entire Bible.

Charles Spurgeon, in his sermon:

Let us think of what was in the ancient ark of the covenant, for all that was in that ark as a type is to be seen in Christ our heavenly covenant ark above.

In that ark, if you and I could have gone into the holy place, and have had our eyes strengthened to look. we should have seen, first, God dwelling among men.

John Wesley, makes the connection:

"...between Christ, on the one hand, and the mercy-seat of the ark of the covenant, on the other, which, as a propitiatory covering, was "a type of Christ the great propitiation" (The Theology of John Wesley: Holy Love and the Shape of Grace)

Charles Henry Mackintosh, from The Mackintosh Treasury:

Thus we perceive what a marked type the ark of the covenant was of Him who magnified the law and made it honorable - even Jesus the Son of God ....

John Nelson Darby, in the synopsis of the Bible:

The ark of Jehovah passed over before the people, who were to leave the space of two thousand cubits between it and them, that they might know the way by which they must go; for they had not passed this way before. Who indeed had passed through death, to rise beyond its power, until Christ, the true Ark of the Covenant, had opened this way?

If you look hard enough you can always find similarities. The correspondences between Mary and the Ark of the Covenant remind me a lot of Islamic arguments that Muhammad was the prophet Moses prophesied about in Deuteronomy 18:18-22 rather than Jesus.

According to Muslim apologists, there are many similarities between Moses and Muhammad, many of which do not apply to Jesus (source: whyislam.org):

• both were prophets
• both had normal human parents
• both had wives and children
• both had normal deaths
• both had spiritual and legal missions, and both served as both a prophet and governor
• both were generally accepted as leaders by their people, unlike Jesus
• both waged war

But according to Christian apologists, most of these miss the point. While they may be true, the important characteristics of Moses were not that he had a wife and children. Instead the similarities we should be looking for are things like this (source: answering-islam.org):

• Moses performed miraculous signs
• Moses spoke directly with God
• Moses was assured of his calling by God directly, rather than by his wife
• Moses's revelations did not need to be abrogated by himself
• And unlike Muhammad, Moses never thought he was demon possessed, never became delirious, and never spoke words of Satan (and the link above contains other disturbing claims)

For most Protestants the points of similarity given in the question between the Ark and Mary would look like you're grasping at straws. The similarities are real, but unimportant. The important things about the Ark of the Covenant are the following:

• On the day of Atonement the High Priest would take the blood of the bull and goat (which were sacrificed as sin offerings), and sprinkle it over the Ark, making atonement for the nation. This soteriological role points only to Jesus. Some Catholics call Mary Co-Redemptrix, but that is not even official Catholic Dogma!
• The cloud of God's presence was positioned above the Ark, demonstrating that God dwelled within his people. But they were cut off from him, behind a curtain only one man could pass through once a year, outside a temple restricted to the priests, behind a system of expensive and bloody sacrifices.
  Mary bore Jesus the Son of God, who came to dwell among his people (John 1:14). God's presence at the Ark is a tiny shadow of his presence in the person of his Son, but as such the Ark is pointing to Jesus, not Mary. I don't think the Ark could really be considered to have ever carried God, rather it was the location where God descended to be with his people. If anything, the way in which Mary led to God dwelling with his people is far beyond what the Ark did, and comparing her with the Ark is a negative comparison.
• God was holy and so the Ark was holy. But almost all protestants reject the idea of Mary's immaculate conception believing instead that she is a sinner like the rest of us. There is no comparison between the Ark's holiness and hers. Mary's righteousness is imputed to her through her faith in the gospel, not because she carried the embryonic Jesus.