Could someone belong to The Tribe of Ephraim, and still be considered a literal descendant of Aaron?

I don't know about Mormonism, but in the Bible the answer would be: Yes, in two ways.
#1 - a woman who is descended from Aaron marries someone of the tribe of Ephraim, thus becoming a member of that tribe
#2 - someone descended from the married couple mentioned in #1 would be a biological descendant of both Ephraim and Aaron and would be of the tribe of Ephraim

Ephriam was a son of Joseph. Aaron was a son of Joseph's brother, Levi. So the answer is no.

Hypothetically the answer to your question is YES, But there is a real problem with your question.

The official genealogical records of the tribes of Israel were destroyed by Rome during the siege and sacking of Jerusalem in 70 CE. Contrary to the orders of the Roman command, the temple was totally destroyed. As a result no one who claims to be a Jew today has any idea as to what tribe if any they belong to. In effect the Jewish people exist only in the imagination of those who carry on tradition.

The Jews have no priesthood and no temple. A synagogue is only a meeting place, A rabbi is only a teacher. Sad.

That's strange. Aaron is descended from Levi, (where the Levitical priesthood came from). Levi is the brother of Joseph who had two sons, Ephraim and Manasseh. Levi is their uncle.

Mary's mother, from the tribe of Levi, married Mary's father, Heli, from the tribe of Judah, so it's possible if someone from Levi/Aaron married into the tribe of Ephraim.

genealogy makes no difference under Jesus's new covenant.

only if they were female could that be