Yes, if you have nowhere else to go, but it's a last resort and there's definitely a high chance of fines or more serious consequences, especially if it's an active base with sensitive material or operations.
In this case, it's not about the FAA. An military base can choose not to prosecute once they investigate, but don't assume that they are just fine with strangers landing. Emergencies can be staged and, as stated, if there are sensitive combat and intel operations ongoing then it will be a serious incident.
This is no different than calling search and rescue to save your life, and then getting a bill afterwards. Still an emergency, and still has consequences.
It is a crap shoot, based on optics, and partially based on real data. You have to hope your investigator, or boss, sees the data the same way you did....
You made the opposite choice, lose your airframe and your life, and then you should 'clearly' have made the other decision, because the data's in...