Was "No prophet ever came out of Galilee" sarcastic?

It's incomprehensible to believe that the prophets of Judah who had studied Scripture their whole lives would have made this mistake. Elijah, Micah and Joel plus three more prophets all lives and prophesied in Galilee. The mistake was engendered by a poor translation. Out of all the languages extant in the 1st century, only Aramaic carries no articles such as "a" or "the." Translating word for word often leads to lack of context and syntax. Given that, the translator had a 50-50 chance of getting it right. He didn't. He also didn't seem to understand the implication of his work. The passage should have read: "the prophet does not come out of Galilee," that is, the prophet (Messiah) Moses talked about that would come. Also, the same prophet the Pharisees asked John the Baptizer about when they asked him if he was Elijah, the prophet or the Messiah. The only logical explanation for this error is that the original passage was in Aramaic and later translated into Greek incorrectly. All the other languages (Hebrew, Greek, Latin) have articles which would have made the priests' comments abundantly clear. Aramaic primacy.

It would seem the of context the Pharisees comments are about rejecting Jesus regardless of where he’s from.
Any negative comment that can be believed by those to whom they are speaking in order to get them on their side and deny Jesus as the Christ because it came from the experts , Pharisees would be the root intent.
Nicodemus became the voice of reason which was also rejected based on his being from Galilee.
This was pure bigotry.
Essentially John was showing not the Jews but the leaders of the religion as the cause for his need to return and offer himself up.
Jesus was about rejecting the law as it was applied w malicious ungodly like intent.
Mincing words when it becomes the hub around which we argue truth of Jesus as the Christ makes us no better than the Pharisees.
If the words are of God , then the understanding of them is of God also.
I suspect too that the Pharisees were no better than Pharaoh on this one.

In all, I believe that if someone hates you so much, even if you swim in the river they would complain you spread dust on them. The authorities hate Jesus and wouldn't want to associate with him in anyway not to mention Galilee where they ignorantly believed nothing good could come out of. V52 shows clearly that they were against the truth only because they foolishly believed Jesus came to take over their authority and deny them of their worldly benefits. Prophet Jonah , Elisha, Hosea and others came from this city. It is unbelievable that in their long time in the study of the books. They still denounce the truth just because they didn't agree with Jesus even when Nicodemus tried to be positive of him they ignored him.

At issue here is not whether the Pharisees’ comment is technically correct – as the OP notes, it is easily proven false as a statement of fact. N.T. Wright’s word study of their particular verb and its possible, extended, theological associations is interesting but also a digression.

Rather, John is intent on showing that Jewish leaders, centered in Jerusalem and Judea, rejected Jesus, while Galileans and others accepted him. This dichotomy is also apparent in the Johannine symbolic use of geography generally, setting Galilee against Judea. John 7:52 presents the Pharisees as sneering and derisive, sarcastic, though not in the sense of ironic. Their comment is intended to bolster John’s negative portrayal of ‘the Jews’, and more specifically Jewish leaders, in contrast to Nicodemus who believed.

The intention of this verse, then, is not centered in its accuracy or falsity as a factual statement but in its contribution to John's larger narrative portrait of the Jewish opposition to the gospel (e.g. 4:1; 7:32; 8:13; 12:42).

Their question is not just about whether a prophet can come from Galilee, but verse 42 gives more info about their reason for doubting Galilee as the source of the 'Christ'. The Christ should come from David's line and from Bethlehem (prophecy from Micah 5:2). Herod ordered the murder of all the boys in Bethlehem, so there would not be any men from Bethlehem around Jesus' age. Even though Herod died before Mary & Joseph returned from Egypt, Joseph still feared Herod's son, who was then ruling in Judea, and God warned Joseph to go to Galilee instead (Matthew 2:19-23). Joseph and Mary probably didn't broadcast that Jesus was really from Bethlehem because of their fear (and because of God's warnings).