Honestly, you'd be in a much better position with an actual offer. With just a little bit of skills and some luck, many can get to a second round - but you need a lot more than that to get an interview. Just knowing you are in the final round at McK doesnt tell us much besides that you have a solid resume and can do math (cf. PST).
Now, once you have an offer in hand... different story.
After my interviews, I got a verbal offer from BCG - but with a delayed start date due to the timing (experienced higher here). BCG never asked me if I had "final rounds" with Bain or McK - no, they were only interested in knowing if these 2 would make me a full time offer, in which case BCG would bring me in right away. In other words, the bargaining chip only had value of one of the two large competitors actually wanted to higher ne, not if they merely were 'talking' to me.
I suppose a 2nd tier or boutique may (emphasis, 'may') look at you differently if they know you have a final round at McK - but Bain/BCG... highly unlikely at this stage. Sorry