Imagine Halo Wars, one of the best strategy games ever, on your handheld device! Play anywhere (with Internet access or offline), anytime! This would be an amazing app and I personally think it would be worth the time to make.
It would be easier to reformat everything from the 360 disk to be able to play it on the Vita than it would be to do this. Microsoft won’t ever release the game on a Sony console, so you might want to learn how to code and get some free time.
This might be a possibility in 5 years or so since affordable (and Microsoft-neutral) handheld processing power currently resembles the Dreamcast. Maybe a forums app would be good, but implementing the game across mobile platforms is nearly impossible and would take too much money to be profitable even if they could do it. If they took steps to pioneer the next stage in handheld gaming, it could be a very good idea, but battery life would be in question (thus making it grounded-gaming, not mobile). How much trouble do you think Microsoft is willing to go through to license their game on an Apple product too? They’d just release it on Windows phones. Maybe it’d spice up their less than stellar app library.
I don’t think so.
I think it would be cool to see it on Vita. Sadly, that’s impossible 
However, I like your train of thought. Problem is, as Legskindal said, it wouldn’t work. It would cost too much, and who knows how well an iOS device could run it? Just look at Batman: Arkham City Lockdown. I’ve only ever made it past the loading screen for that twice. I really don’t think this would work.