As a mgt consultant, I think I can give some of my OWN views on your question:
1) Yes, of course. Mgt Consulting firm welcome all bachelor degree holders, but better students from top universities, or you can demonstrate your special skills or potential during interview. (note: the industry is very demanding. You have to keep up yourself with the market need. The "market force" will eventually push you to pursue your further degrees and so on)
2) Since the mgt consulting is a very special platform, for a new comer, the consulting firm's brand name may not very important to them (you) as long as the firm is really doing mgt consulting business. The top issue you have to concerned is whether you can learn from the consulting firm (Mgt consultant firm is a special industry in China and many of them are actually doing low end consulting business--though they are making money)
3) I would say--YES! It is worthwhile for you to stay in this industry, but it is very tough and not easy to get along with it on your career journey.
I have a topic for this issue which maybe helpful to you:
對有興趣或剛當管理顧問的朋友一點小建議
https://bbs.pinggu.org/thread-2758624-1-1.html