I'll start with the caveat that I do not have direct experience with Fast Track. That being said, here are a few things to keep in mind:
1. BCG is growing extremely fast in most regions, and this growth is often constrained by the staffing.
2. BCG has also been reaching out aggressively to its former employees to see if we'd come back. In other words: there is plenty of work
3. In any case - promotions are typically based on your performance level more than on the office needs or amount of work available. Sure, promotions may be a little delayed if business is particularly slow, but again we are nowhere near this situation now
4. Your concern re. network & sponsors is probably more valid. In my opinion however, this is mostly useful when (a) you underperform, and or (b) when you are looking to be elected Partner - neither of which are relevant to you today
5. All this being said... who cares? Get in BCG, get the 3 letters on your resume, learn everything you can while there and do the best you can. Your career will take care of itself. And what if you don't get the promotion after 6 months? In all likelihood, it will just be postponed a little bit but the experience will have been more than worth it in the worst of cases.
Congrats on the admissions, good luck & welcome to the BCG family.
G, ex-BCG Dallas