First of all it's important to understand that consulting firms act more rationally than most other firms (should not be that surprising, but worth mentioning anyway), so if it makes sense business-wise, they will probably do that.
So let's look at your question now. Yes, indeed that is a possibility that well-performing interns might receive full-time offers - maybe not automatically straight away, but potentially with a fast-track recruiting process.
That being said - consulting firms are also profit-oriented companies and partners want to take home a reasonable amount of money (yes, ethics exist too.. but let's keep it simple for now). If demand on HR market (depending on consulting projects and required skills) is exceeding current staff - drop-outs + well-performing interns, then additional recruiting will take place.
Side-note: For now it's difficult to imagine that MBB will completely stop recruiting activities since many bright young candidates are somewhere out on the HR market. However, the bar for getting interview invitations as well as for receiving offers will be rising.
Hope that helps - if so, please be so kind and give me a thumbs-up with the green upvote button below!