You certainly can. Here's some of my thoughts on playing on console, for your consideration:
First: You're missing the ability hotbar. That might actually warrant changing the route, as any switching of abilities is time lost.
Second, and this is something I haven't tested a whole lot, but there's some "sticky ledges" in out of bounds areas. In PC you clear these by holding W and crouching and uncrouching. On 360, I've tried it a couple times and not been able to do it. It could be that since crouch is on the stick, I may have been letting off the stick briefly. Or, it could be that it's actually not possible on 360 for whatever reason. If that's the case, then you'd have to take a different route through a few parts. Off the top of my head, the oob to choras den isn't possible. There's two sticky ledges in that one, and there's an alternate route to bypass the first, but the second isn't avoidable to my knowledge.
In short, yes, you can definitely speedrun this on console, and I'd be interested to see how the route turns out.
Awesome! i'm gonna start running this soon, and i will work to figure out the route that is best for console
If you want, you should try talking to aleck47, he has a decent amount of experience looking into the console version of the game from a speedrun capacity: https://twitter.com/aleck47goesfast
Just noticed this, and it's basically as YNH said. The main thing I'd add is that if you go too fast in certain areas, like the place on Noveria where you first encounter Rachni, the game will incorrectly load triggers (or not load them at all) and softlock.
Starting with glitchless honestly wouldn't be a bad idea - then see what you can do. Quite a few of the skips are still possible, but others aren't, and the Peak (whatever the number is) skip I only managed once in a good couple hours of attempts.
