Yes, it can be done. For example for Debian (other distro's i don't know, some are a bit touchy when installing to a pendrive).
Go for expert-mode (might work with the usual mode too). During partitioning point it to the stick (if necessary choose "manual partitioning"). At the end of the installation you will be asked if you want to install grub: choose yes. You will be asked:"to the mbr". Choose: "no" You will be asked:"where then?". Point it to the partition of the pendrive.
Make sure the PC('s) are able to boot from USB. Else check this:
That is the main problem, besides that its a usual installation.
PS: i don't want to push you to use Debian for this. I simply don't know how and if (at all) it works for other OSes. I think it should.