That's a very good question, and also a crucial one. But, interestingly enough, my answer is... no. And my reason is, generic controllers don't have the same button and stick definitions as an Xbox controller. If I start Cattle Crisis with a generic controller, I'm going to have to go through a trial-and-error process, to figure out which analog sticks, d-pads, and buttons have moves automatically imposed on them. This is a treacherous thing to do, because in some games, you have to also unlock moves. So, even if a move doesn't feel like it was successfully imposed, it may actually be so. If a move isn't imposed, I'll end up having to go into a profiler program (like JoyToKey) and having to manually add the move.
In the amount of time it took to play trial-and-error (followed by manual button entry) I could have just taken the game's keyboard defaults, plugged them all into JoyToKey, and started Cattle Crisis for the first time, without struggle. Being able to create your own controller layout is also one of the advantages that PCs have over consoles.
This year, I started an entire site (conflexgames.com) which is dedicated just to PC games that are guaranteed to cooperate with JoyToKey layouts, if you take a game's keyboard defaults, and plug them into that program. Finding a game's defaults is really easy - just scan the barcode with your phone. Conflex Games is okay with controller imposition, if it's specific to Xbox and PS controllers.