How hard is the move from BB to Boutique for S&T

I secured a summer analyst role at a BB for S&T, but am flirting with the prospect of joining a boutique full-time, particularly those with prop trading. I currently attend UChicago and was wondering if this move is common, or is it extremely hard to do. I understand that prop trading firms tend to go for people more in terms of how quaint they are rather than their overall background, but I am majoring in Math. I know it also depends on the desk I'm at during my time at the BB, but my program is rotational, so if I am at a relevant desk, would that help? Even if I'm not, I figure that I could just say that unlike other candidates, I've been exposed to multiple desks, so I understand what my strengths and weaknesses are (in terms of desks and products) better than those who didn't partake in a rotational program.