It never hurts to ask! The recruiter had the hiring panel take a look at my app and was able to get me a Meet the Chiefs invite. Unfortunately I'll be unable to attend since my flight schedule just got changed and its smack dab in the middle of a mil exercise week.
I was very impressed with how quick and professional the responses were and the fact I got a response at all.
The hiring panel informed the recruiter that I had enough multi-engine TPIC (fighter, ~1250) to receive an invite. So for any mil guys that are low on TT - Don't let that keep you from trying to go to Spirit!