Is regex with backreference still able to be implemented by finite automata?
No, it doesn't. With backreferences, it is trivial to write a regex that matches exactly the standard textbook example of a non-regular language, $\{ a^nb^n \mid n \in \mathbb{N} \}$. A finite number of states can only distinguish between finitely many different prefixes in $a^*$, so it won't do.