Kind of.

Tolkien presented hobbits as relatives of the human race,[T 4] or a "variety"[T 6][11] or separate "branch"[T 7] of humanity.[11] In Tolkien's fictional world, hobbits and other races are aware of the similarities between humans and hobbits (hence the colloquial terms for each other of "Big People" and "Little People"); nevertheless, hobbits consider themselves a separate people.[T 8]

https://en.wikipedia.org/wiki/Hobbit#Description

Considering the vastly different physical and mental characteristics I think it's probably more fair to view them like we view Orangutans and Humans as all belonging to one taxonomic family but not being the same species. In that regard hobbits are not men.

Edit: or probably more accurately, a genus https://en.wikipedia.org/wiki/Homo in which case I think I concede you're right after all, no matter how much I don't like the thought of hobbits being men