Deferred MBA Likelihood (HBS, S, Penn, etc.)

Hey guys - was wondering if I could get some advice/ hear some experiences regarding deferred MBA programs? I am currently a senior (non-diversity) at a target school and am planning on working in the PE industry (a well-known firm) right after college. I have some extra free time on my hands right now and was wondering what the likelihood/chances are for me if I were to pursue an MBA (deferred). Does it make sense to do that? Are my chances harder given I have zero work experience? Should I only be applying to the top programs? Would love to hear some insights and/or advice.