NH enforces. You could get pulled over soon or it could take a while, but why give a reason to get pulled over. And if you do get pulled over for something else, it is just one more thing you are doing wrong and for which you won't get the benefit of the doubt (you are presumed to know the law, so ignorance is not an excuse).
You have local, county and state police all enforcing the law. In NH, the county sheriffs do not seem to do that much traffic work, but you will occasionally see them pull people over. Locals from one town to another may vary in their enforcement. The state police are more consistent, but individual officers may vary. Certainly the one running laser and trying to point it at your license plate will notice it is missing.
Chances are pretty good that if you do get a ticket, you will be able to get the ticket dismissed if you fix it and demonstrate the fix to the court. It would be helpful to have an excuse, like the plate fell off.
Good luck. I run front plates even though I would prefer not to and have previously not run one when I lived in states where either one was not required or there appeared to be no enforcement.