I'm not sure if it would "explode," but you could be injured badly, or worse.

Years ago, I had an accident with an M-16/AR-15 weapon. Like an idiot, I listened and was firing it left-handed, as I was told (since I am naturally left handed). I may not have had it against my shoulder correctly, or it may have just happened, but there was a 45 degree "stove pipe" and one of the locking bolts struck the primer, setting the charge off. The projectile fired into the air, but the primer ruptured and the hot gases blew back across my face. Needless to say that I survived, but it was a mess. My left eye and ear suffered damage that lingers today. If the bolt would shatter in the Nagant, it could be forced backward with enough for to injure or kill, but this wouldn't be an actual explosion, I don't think. It would just be the natural law of firearms being applied in the wrong way.

For the weapon to explode, I would think that the barrel would need to be blocked, closing the front door, and the bolt closing the read door, leaving the gases no place to go. This would cause the chamber to fail to contain the pressures for the time, and boom. As long as there is some form of vent, even if incorrect, the chamber should hold the pressure if it can vent fast enough. What you get with a partially blocked barrel, would happen. The sudden pressure would exceed the capacity of the chamber and... In most cases, however, you have a margin of safety to protect you. Unless the bullet is too big for the barrel, closing the front door, even variations in powder charge or primer will just cause a change in the projectile, and only stress the weapon. Unless repeated, these stresses shouldn't be so severe as to be dangerous. This is why reloading datum need to be followed carefully.

You should be able to purchase a gage that will allow you to check the firing pin, as well as one to check the head-space. I know with the M16 series you can, anyway. If not, a gunsmith should be able to check and see if it is safe to shoot, which you should always have done when purchasing a used weapon, and more-so with a war relic of this age. I would think, however, that you might be able to "test" it with a homemade gage, to see if it is very bad, but I don't advise this to you due to the risks involved. In my "dirty past" I have had to press such weapons into service and do my best to insure they are safe even then. If you can find a qualified gunsmith, I would suggest getting him/her to check it out. Safe, not sorry.