I think if the rim is bent they'll have to take the tire off, but other than that they can do it with the tire on there, but the wheel does have to come off the car (no you won't need an alignment). I had a pretty nasty gash on mine and the guy just took the wheel off, did the work in about an hour, put the wheel back on and I was on my way.

 

I don't think my wheel is bent? is it?

 

Your rim doesn't look as bad as my rim was, and my rim wasn't bent so I think you're ok.