This is directionally right, yes: MBB wants good people, and will train them as needed. Best way to get admissions is to get an interview and crack the case. With a PhD + MBA, you have a solid background. Hopefully one of the institutions at least is a target school. If not, you may need to do some networking. But again, no need for specific work experience ahead of MBB.
For Tier 2 and Boutiques, actual expertise will be more important though even there, they'll typically train you.
PS: MBB does sometimes hire specialists for specific experienced hire positions, but you dont seem to qualify yet based on what you write.