Last year, we received a notification that my daughter's NASS spot was about to be taken away due to non-payment, even though our check had already cleared the bank! I'm sure that's not too common, but mistakes can happen. If your check has been cleared for more than 2-3 weeks without receiving your final acceptance letter (the one that says that you should show it and a photo ID to be allowed on the Yard), I would follow up with a phone call.
Cell phones are fine to take, but don't expect to have much time to call home. My daughter got off a call the first night, but had no time after that. That may vary by squad.