Perhaps, but it is hard to say. Obviously most major hospital systems (i.e. UCLA or USC) are generally going to prefer their own students over ours. We mainly rotate through community hospitals in the greater LA area. Something to keep an eye out for, we may or may not lose one of our larger rotation sites (ARMC) as they opened their own school.
For third year you likely won't rotate at such places, however for fourth year you make your own schedule (you have to meet requirements but you choose where you go) so it is all on you and your ability to secure spots at those institutions. But yes, plenty of our students rotate at such places 4th year.
I hope this helps, best of luck on your journey!