tl;dr

Emanuel Swedenborg (1688-1772) agrees with Oneness Pentecostals and other modalists in affirming the full divinity of Father, Son, and Holy Spirit, while denying that they are three persons.

This has led to the common error of labeling Swedenborg and Swedenborgians "modalist."

However, Swedenborg rejects the essential, defining modalist doctrine: that the Father, Son, and Holy Spirit are three different modes or manifestations of God to human beings.

Swedenborg, and Swedenborgians, are therefore not modalist in their doctrines and beliefs.

Now for a fuller answer to the question.

First, we need to define God from the modalist, Oneness Pentecostal, and Swedenborgian perspectives.

The Sabellian or Modalist doctrine of God as Father, Son, and Holy Spirit

As defined in the Wikipedia article linked in the question, this is the Sabellian or modalist conception of God as Father, Son, and Holy Spirit:

Sabellianism in the Eastern church or Patripassianism in the Western church (also known as modalism, modalistic monarchianism, or modal monarchism) is the nontrinitarian or anti-trinitarian belief that the Heavenly Father, Resurrected Son, and Holy Spirit are three different modes or aspects of one monadic God, as perceived by the believer, rather than three distinct persons within the Godhead--that there are no real or substantial differences among the three, such that there is no substantial identity for the Spirit or the Son.

The Oneness Pentecostal doctrine of God as Father, Son, and Holy Spirit

As defined in the Wikipedia article linked in the question, this is the Oneness Pentecostal conception of God as Father, Son, and Holy Spirit:

The Oneness doctrine . . . states that there is one God, a singular divine Spirit, who manifests himself in many ways, including as Father, Son, and Holy Ghost (a.k.a. Holy Spirit).

The Our Beliefs page of the website of the United Pentecostal Church International, which is the largest Oneness Pentecostal denomination, expresses its basic beliefs about God in this way:

There is one God, who has revealed Himself as our Father, in His Son Jesus Christ, and as the Holy Spirit. Jesus Christ is God manifested in flesh. He is both God and man.

Emanuel Swedenborg's doctrine of God as being Father, Son, and Holy Spirit

In True Christianity #163, Swedenborg defines the Trinity of God in this way:

1. There is a divine Trinity, which is the Father, the Son, and the Holy Spirit.
2. These three, the Father, the Son, and the Holy Spirit, are three essential components of one God. They are one the way our soul, our body, and the things we do are one.

(Note that although Swedenborg regularly uses the word "Trinity," by traditional Christian definitions of "trinitarian" he is non-trinitarian because he rejects the idea that the Trinity consists of three persons, but states instead that the Father, Son and Holy Spirit constitute a single divine person who is the one God.)

Swedenborg's doctrine of God is incompatible with, and denies, modalism

Swedenborg's theology agrees with Oneness Pentecostal doctrine in denying that there are three persons of God, denying that there was any "Son born from eternity," and affirming that the Son (and the Holy Spirit also) came into existence with the birth of Jesus Christ.

However, Swedenborg's theology rejects the defining characteristic of modalist doctrine, which is that the Father, Son, and Holy Spirit are three different modes of God, or three different ways that God manifests himself to humans.

Instead, Swedenborg's theology states that:

1. The Father is the transcendent, unknowable soul of God, of which we can have no direct knowledge or experience at all.
2. The Son is the human body or visible appearance of God--and, since the Incarnation, is the sole avenue by which the Father is known to human beings.
3. The Holy Spirit is the divine truth and power flowing out from God, and in effect is the manifestation of God to human beings.

Swedenborg calls this a Trinity of "essential components" (Latin essentialia) of one God.

These three are not different modes or manifestations to us of some underlying divine Spirit.

In Swedenborg's system, the Father is the underlying divine being, and is not perceivable by us at all. We finite humans are incapable of grasping or comprehending the infinite divine being of God. Only through the Son can we have any knowledge of God. And the Holy Spirit is the knowledge and power of God as it flows out from the Son, enlightening us and giving us spiritual life.

So instead of being modes or manifestations of God to human beings, the Father, Son, and Holy Spirit are more in nature of parts or constituents of the divine being. (The Latin word essentialia that Swedenborg uses to characterize them is somewhat difficult to capture and convey in English.) They are certainly not different appearances of God, as modalism and Oneness Pentecostals hold.

In Swedenborg's theology, Father, Son, and Holy Spirit are entirely distinct from one another, and cannot change into or appear as one another. Together, these three distinct but fully united "components" form a single God, in one divine Person, whom Swedenborg calls "the Divine Humanity" and "the Lord God Jesus Christ." The three together are God just as our soul, body, and actions are us. There is no other underlying divine Spirit of which they could be "modes."

Swedenborg does state that God relates to humans in various roles, such as King, Priest, Prophet, Savior, and Redeemer. However, according to Swedenborg, Father, Son, and Holy Spirit as used in the Bible are not roles, and thus are not modes of God. Instead, all of God's roles come from the Father, and are expressed by the Son through the Holy Spirit.

It helps to understand that Swedenborg did not interpret "Father," "Son," and "Holy Spirit" as literal terms, like our human fathers, sons, and breaths (which is the meaning of "spirit"). Instead, he saw them more as metaphors drawn from human concepts and experiences that the Bible uses to express deeper spiritual and divine realities about God.

For a fuller explanation of Father, Son, and Holy Spirit from a Swedenborgian perspective, written for a popular audience, see my article, Who is God? Who is Jesus Christ? What about that Holy Spirit?

For Swedenborg's own extensive presentation on the Trinity in one Person of God, see True Christianity, volume 1. (This link leads to its page on the publisher's website, which offers free downloadable PDF and EPUB versions, in addition to print and Kindle editions for sale.)

Please note: Although Swedenborg provides an extensive biblical basis in True Christianity for his doctrine of the Trinity, I have made no attempt to present it here because it is outside the scope of the question. I respectfully request that you vote this answer up or down based on how well it answers the question asked, rather than on whether or not you think Swedenborg's doctrine is true (which is off-topic on Christiainty.SE) or on how well I have supported that doctrine (which is not the purpose of this answer). Thank you.