The answer is: Maybe.
Here's why:
As you know, the AR-15's cam pin rides in a diagonal slot in the bolt carrier. This is the camming surface that, when the bolt is cycled, allows the bolt to lock and unlock inside the splined receiver extension..
Remove the cam pin and the bolt no longer locks or unlocks. Since it must be in battery for the firing pin to protrude enough to fire, the bolt head will end up in the firing chamber area, but not rotated so that its locking lugs engage the splines.
Thus, when fired, the entire chamber pressure of 50-60 thousand PSI is pushed back against the bolt, instead of the bolt being locked to the steel-splined barrel extension designed to hold the bolt closed against those pressures. Gas pressure and the recoil of the shot being fired are all focused on that unlocked bolthead, which will push the bolt carrier backwards both prematurely and with significantly more force than it was ever designed to take. Instead of the controlled bolt unlock, you've got the equivalent of blowing a piston out of the cylinder of a car without the piston rod. It is uncontrolled force significantly greater than the aluminum receiver was ever designed to withstand.
The bolt carrier will be driven straight backwards against the buffer and into the buffer tube as usual, but a whole lot harder than if the cam pin were in place and the bolt were the captured unit it is supposed to be.
But how much harder?
That, my friend is the 64 dollar question, because it depends on quite a few factors, not the least of which is the nature of the ammunition you're using, which includes powder charge, powder burn speed, and even the weight of the projectile, as well as the weight of the rifle's bolt carrier and the buffer at the other end of the bolt carrier, not to mention the amount of wear on the buffer spring.
At the very least, it will transfer that incredible force to the buffer, which, at the end of its travel, slams into the back of the buffer tube while the gas key slams into the top of the lower receiver ring at the front of the buffer tube -- a relatively thin piece of metal.
So now your safety depends upon the strength of two pieces of aluminum not designed to ever take that level of stress.
Will it explode? Your guess is as good as mine. If you have a well built, solidly machined billet receiver, the chances are better it won't; But that's no guarantee. If you have a cheaply-made, cast receiver that wasn't cast quite properly, well, russian roulette might be safer.
Though "explode" isn't quite right. "Experience a catastrophic failure" would be a better phrase, because most of the damage would be expected to be done by the velocity of the bolt carrier hitting things, not the expansion of gases...however, because those gases are are being spat out of an unlocked firing chamber, focused straight backwards against the bolt, and after the bolt leaves the chamber area the gases expand into the aluminum receiver, it could very well look like an explosion.
What could most likely happen is that you could end up with a piece of receiver in your face and/or chunk of bolt carrier in your face or arm, while a great gout of fire belches out the ejection port and down into the magazine. If you've got more ammo in that magazine, there's also a chance that those expanding hot gases could cause one or more of your rounds in the magazine to "cook off" while sitting against one another. Not a good day.
This question was also asked on TheFiringLine forums. A link to that thread is provided in the source area.
Can I guarantee you'll experience a catastrophic failure? No.
But removal of the cam pin will, if the rifle is fired, put significant force upon components of the rifle that are not and were never designed to take it. And when you do that, it's really only a matter of time before the safety margin of the design fails.
Could be the first time, could do it a hundred times and not experience it; Every rifle build is different.
But the risk of catastrophic failure is definitely present.
Here's what one might look like (Caution, foul language): http://www.youtube.com/watch?v=tWygoxV_ApM
The failure happens at 1:02 in the video. Watch carefully and if you like, frame-by-frame it. It happens very, very fast. While this particular failure was not attributable to the cam pin (it was apparently bad ammo, as you will see in the video), a catastrophic failure is not something you want to experience, and it's not all that predictable. Rifles have blown up in the hands of soldiers on the firing line and disabled them for life. Others have been more fortunate and have walked away with barely a scratch.
Given the amount of energy involved, it's not a risk I recommend you take.
Ever.