Is there any way to fix a tub faucet that has pulled away from the wall without having to tear out the tile? Can the exposed pipe be "covered up" with some kind of fitting to make it look like it didn't come loose?

depends... look underside the spout for a little grub screw hole... and a scratch on the pipe if it's copper. if that scratch is there and the pipe itself doesn't wiggle, loosen the screw (either a hex or a bristol spline wrench depending on maker), push the faucet back to the tile on top of a little fresh caulk, and tighten it up.

if not... I'll tell you what happened, and you can make the call.

the actual faucets where you turn on water are connected to supply pipes, outlet pipes up and down to the spout, and are (should be) screwed to a brace within the wall.

if this actual control unit is pulled loose, all those pipes are bent now. the connections to them are bent as well, and kinked. eventually they are going to leak (copper) or break (plastic, PEX.)

when that happens, you've got a flood behind the wall. wrecking everything to the sides and below.

you've got two choices if this is a faucet problem instead of the spout. one, punch a hole behind the control in the other side of the wall, insure the plumbing is (hopefully) undamaged, or fix it if damaged. then reconnect the controls to the brace. since you aren't going in from the side in which the original screws were used, probably need to use hose clamps or screw-on "pipe tails" that bolt to the pipe and then nail or screw to the underside or top of the brace.

or you have to rip up the front, replace the control if badly damaged, and redo at least the front side tile job.

if this happened because somebody was falling and grabbed the controls... better put up handrails.

Just grab the faucet and pull gently in and out. Does it move?
There's three differant ways a faucet can be attached to the pipe coming out of the wall, if it's the type that just slips over the copper tubing then tere will be a set screw on the bottom side of it. All your going to see is a hole the screw is recessed. Loosen the screw and slide it back in place.

It the whole spout and the tube move at the same time then sometings came loose behind the wall.
There should have been an access panel on the back side for cases just like this.
Go to Lowes or HD and pick one up, do not pick the smaller one. There made so you can just cut a hole and they just snap in place.
Once the holes cut you should be able to see if the block of wood holding the faucet in place came loose.