Chasing up applications

If a university says it plans to get all its applicants interviewed and accepted or rejected within five weeks, and it's been two weeks since I applied and they haven't been in touch except for an automatic email acknowledging my application, can I start badgering them yet? I've got two people agreeing to supervise, so I should at least be called to interview (no?), and I need it to be sorted quickly, as this silly institution will only consider candidates for funding if they've sent out an offer by the funding deadline. That's right - applicants can get punished internally for slow admin staff! The five week deadline would also take me three days beyond the last funding deadline