...Whoa. I actually posed the question of "What would happen if Bowser tried to enter one of the pipes that led into his body?" on another forum a while ago, and after receiving a few comments, I decided to delve in and attempt to solve the paradox myself. Below is my dissertation on the subject.
(MAY CONTAIN SPOILERS!)
Well, to answer this question, we need to know a little about how warp pipes work. It's clear that, while some pipes are merely connected tubes like the screen-scrolling pipes found in Super Mario Bros. 3, one end of a pipe doesn't need to be physically connected to the other; while it's possible that the name "warp pipe" just comes from the fact that they take you from one place to another so fast, pipes actually appear to, in fact, use some sort of teleportation mechanism. We've seen numerous examples of this throughout the Mario series. Obviously, there's the pipes inside Bowser that lead to other locations in the Mushroom Kingdom - they don't go through Bowser at any point. In Super Mario Galaxy, as well, there are a few pipes on the planetoids that, when entered, take Mario to a completely different planet. There's no visible connection between the two planets, indicating that entering the pipe simply teleported Mario to the other location.
So, according to this theorem, if Bowser entered one of the pipes that led into his body, he would most definitely appear from that pipe. No grotesque bodily twisting or being turned inside-out involved. But what would happen to the pipe, since it was inside Bowser?
Our knowledge of warp pipes allows us to answer this. When you enter one, your body is transported from Pipe End A to Pipe End B, with no physical stops in between. So, if Pipe End B is inside Bowser, Bowser's body would be transported to a location inside Pipe End B, which would now be located outside his body. Pipe End B would be located in midair when Bowser first emerged from it, since wherever it was in Bowser's body would be above the ground level, but it would presumably fall to the ground immediately under the influence of gravity - or, perhaps, directly onto Pipe End A. Bowser would then fall to the ground as well.
It sounds like Bowser would be safe and unharmed, in addition to having a cool new way to get some of that junk out of his body. But there's one other thing we have to consider. The objects Bowser inhales shrink in size, becoming microscopic and fitting into his body. If Bowser went from Pipe End A to Pipe End B in his own body, Pipe End B's size would be incredibly small. Would Bowser come out miniaturized?
To solve this puzzle, we must look at what happens what objects exit Bowser's body. Unless I'm forgetting something, aside from the Mario Brothers using the pipes to get out, we see three instances of objects exiting Bowser while he's under the influence of the Vacuum Shroom. Broque Monsieur climbs out of Bowser's body after being sucked in while demonstrating how to use Bowser's vacuuming ability in battle; Fawful uses a laser gun-esque device to draw Princess Peach from the Flab Zone; and Mario, Luigi, Starlow, and everyone else inside Bowser are thrust out his mouth by Fawful's last-ditch explosion. The second one doesn't give us much to work with; Fawful's device could work in any way. But the first and last ones provide our answer. Broque Monsieur exits Bowser's body and very clearly grows back to full size, and when everyone is blown out of Bowser, they appear on the platform above Peach's castle in their normal, macroscopic sizes.
According to this property, when Bowser first disappears from his former position and appears at Pipe End B, the pipe is small at first, but then, since it has exited Bowser, it will revert to the size it was before Bowser swallowed it. Thus, if Bowser entered a pipe that led into his own body, the pipe would be removed from inside his body and he would emerge from it at normal size and in perfect condition.