yes!
If 360: install/download your profile onto her console.
Once your gamertag is logged in on her console, it can download any previously-purchased XBLA games. They can stay installed on her console, and she can play them under her gamertag so long as you're also signed in on her console while she plays (using a 2nd controller).
If she doesn't care about achievements/gamertag or doesn't have a 2nd controller, then she should stop gaming, then she can just log in as you and play anything, anytime.
The old 360 rule was: the console a game originally gets purchased on stays forever on that console regardless of gamertag; console that has the owner gamertag signed in can download/play the game but needs gamertag signed in.