>Can you solve a 4x4 with Roux?
Yes. You can use any 333 method you like after reduction.
>Would I still get parity?
Yes. "OLL parity" and "PLL parity" are so named for the CFOP steps in which they become apparent, but they apply to all the common reduction-based methods after reduction is done. In a Roux solve, you'd notice these two parities during LSE (or, if you're a bit more advanced, you can save some time by checking for OLL parity before CMLL). In a ZZ solve, you'd notice OLL parity during EOline and PLL parity during PLL/ZBLL. And so on.
>Could I get the same times as using CFOP for the 3x3 step?
Maybe, maybe not; only you would be able to know. I can't, but I'm also much slower with Roux than CFOP/Petrus/ZZ to begin with.