Is packing multiple prints into the build volume a feasible workflow for powderbed printers? With fdm printers, the 3D object that should be printed can be positioned anywhere in the build volume. But it's only practical to place it on the bottom, because otherwise support material would be necessary.

stereolithography has the same problem. Even though the photopolymer can be cured at any position in the build volume, the result would drift away if it was not held in place by support material.

The powderbed based printers (either powder+binder or any of the laser/electron beam sintering/melting variants) do not have this problem, because they continuously fill the entire build volume with powder. The support material that other printing technologies require is part of the powder based printing anyway. It would be possible to pack the build volume with many prints and print them in one go.

Given that the machines are relatively expensive, it would be economical to increase the throughput. A company that does use such printers heavily could wait a certain amount of time until a few print queued up that fit together in the build volume and only then start the process. Do people do this?
Yes, this is very popular. Look into the site Shapeways and you will see that this is exactly what they do. I've also personally seen a local 3D print shop do this with their machine. It's called batching. I similar technique can be used in traditional machine shops (mills/lathes).