Judging from this meta post, I would believe this isn't possible, as the limit is 6 questions per day. Are there different rules for private beta/public beta?
What is meta?
- Any Stack Exchange user can ask a question
- The community provides support, votes on ideas, and reports bugs
- Your voice helps shape the way Stack Exchange operates
The question limit applies only to part of the network.
I will quote Jeff:
Obviously, unborn site is considered "smaller site". :)