Does anyone foresee any issues arising by advertising or performing this service? I figured I wouldn't have to stress too much about results as it would be done at no cost. Thoughts, suggestions?
Supporting the military is a great idea - but giving everyone who ships out a free shot has the potential to kill your business unless you are really careful.
The army is basically UPS for people - they never stop shipping them out. Before you make the offer you need to know how many people ship out per month, then work out how much time shooting these people will take. More importantly you need to understand the flow pattern. I assume that they ship out in large groups, which, means a potential flood of people all at the same time.
Putting a quota limit or asking people to justify why they should get a free shoot is a PR nightmare. People are going to get turned down and regardless of the way the decision is made they won't be happy.
I would suggest that instead of unlimited free, you offer a discount to military, which enables you support them while at least covering costs. Then, offer unofficial free shoots to needy people like the case in the OP. This gives help where it is needed without creating a feeling on entitlement in others. Then, if you want, volunteer as mentioned in the posts above, where you are one of several volunteers and the load is shared.