First of all congratulations on your job offer and, as a long-standing BCGer, I cannot help but sympathize with your choice of BCG over McK :-)
In general terms, I've seen plenty of candidates asking for a couple of additional weeks to make up their mind about whether or not to accept the job offer (and this also happens with candidates that show incredible enthusiasm and eagerness to start to work over the interviews).
If you made a very good impression during the interviews and you decided to take a couple of weeks to think about the job offer, most likely the recruiting team or a BCG partner will reach out to you asking if there is anything they can do to convince you to accept the offer (this happens especially if they risk losing talent over their direct competitor).
Believe me, consulting companies invest more than 10kUSD to recruit every single candidate and once they find a good one they would do "everything" to convince him/her to accept the offer. I don't see any chance why asking for a couple of extra weeks would backfire on you.