One criteria for membership in the "Mormon Church" might be valid baptism.
There's no such thing as the "Mormon Church".
There's Mormonism, a descriptor used to label the religious communities at whose core is the scripture known as the Book of Mormon.
There's the Church of Jesus Christ of Latter-day Saints, whose members are commonly referred to as "Mormons" (as are members of the FLDS).
But there's no Mormon Church.
Your opening sentence appears to be a very lame attempt at constructing a straw man.
The FLDS derive their authority to baptize through a priesthood line advanced by Lorin Woolley in the 1920s.
Actually the FLDS can trace their authority all the way back to Joseph Smith and can argue that it was the Latter-day sect that moved away from the core tenets of the Church that Joseph set up.
The line is very problematic from a historical and doctrinal view.
The Latter-day Saint line is infinitely more problematic from a historical and doctrinal view when compared to the religion that Joseph Smith set up.
Importantly, if it is invalid, then their baptisms are not valid (D&C 22:1-2) and they could not claim to be "Mormons" in the same sense that Joseph Smith or individuals who have valid baptisms today are "Mormons."
The FLDS members are more aligned to what Joseph would understand as being "Mormon". If anyones baptismal validity needs to be looked at (in light of its comparison to the Church that Joseph Smith set up) it's the Latter-day Saint splinter sect, as they are the furthest removed from the original.
Your question should be "Are Latter-day Saints 'Mormon' in the sense that they practice the religion the way Joseph Smith practiced Mormonism?"
The answer would be no.
For the FLDS the answer would be yes.