Do teams really meet with 3-5 mentors a day ? That seems way beyond the point of being useful. When do you have time to build anything or talk to users ?
It feels overwhelming at times, but it is very useful. It's at the heart of what makes TechStars an accelerator. You get instant feedback on your ideas from great mentors.
You're right that it's hard to build much during the first month. But when the first month is over, you feel very confident about what you need to do. That makes the next month and beyond incredibly productive on product and customer development.
The first 4 weeks is very intense on the business/market/sales plan side of things. It is hard to get work done, you have to squeeze it in whenever possible (night, weekends, etc). The idea is that you probably shouldn't do a ton of work before you have a solid plan in place. After that things slow down and you can focus on coding/traction.
The network is powerful. Alums are generally connected through the mentors and program directors if they aren't in the same class (the cloud class has it's own alumni weekend where the classes got to know each other well).