I got an interview at a MBB for an internship, but I want to try VC beforehand. Would it harm my chances to get into consulting?

Hello everyone,

I am a b-school student who switched from engineering to business one year and a half ago. My motive is to found my start-up some day (but not soon - student loan, etc.). I'd like to get into consulting and stay maybe 3-4 years after I graduate in order to get some experience before starting my own thing. (Consultants make good entrepreneurs, right ?)

I took a gap year to do two six-months long internships, did the first one in business development at a medium-sized company, and got offered another one at a VC firm (which is pretty rare where I come from, there would be only 6-7 active VC funds in the region).
Two days after I accepted the offer, a MBB called me back for an interview. (I did the itw 2 days ago). But even if they offer me an internship, I can't accept it since I have already given my answer to the VC.

So my question(s) is :

Can an internship in VC, instead of consulting, harm my chances to get into consulting after I graduate, for a full-time job ?
Has anyone done the switch from VC to consulting, as an intern ?

Is there any way to negotiate with the consulting firm to postpone the starting date of the internship ? Or even to convert it to a full-time job, with a a delayed start ?

All constructive criticism and answers are welcome.