Vet/Military Recruiting Events for MBA

I’m looking at applying to MBA programs in the near future. I’ve been an Army Reserve officer for a couple of years including about 10 months of active time to the Middle East (one of the non-interesting places), so technically I can check the vet box. But is it kosher for me to be going to these veteran/military recruiting events for MBA programs? Normally I barely tell people I’m in the Reserve, let alone play the vet card. But with schools being so competitive, it helps to get any advantage you can, and that’s the only reason I’d consider it. I feel like it could definitely backfire, though, with those running the event thinking I’m just a shitbag Reservist trying to take advantage of a resource for people who actually did things in the military. Can any of you former military weigh in on whatever I’d look like a tool or not for attending one of these events?