Hrm. I don't think so. Not easily, anyway. I think you can only get the most recent 100 RTs of a target tweet. And, the favorites api is notoriously limited -- like, you can't even collect all of your own favorites. I think you'd need to use an extant archive somehow / somewhere.
Yea :/ Like, to do a real rich analysis of something on here, you have to have started collecting the stream data a few months before you had the idea. Time doesn't work that way, frustratingly. (Or, use gnip or something, which I haven't done yet.)