[NDC]

Would it be possible to drop the old 95 drive into his new XP machine (set as a slave), and have it read it

No problem... If you're luck, you may even be able to run Win95 installed on that hard disk by changng the boot sequence in the BIOS. However, because this is a different mainboard with different configurations, you may run into problems when the new hardware is detected...

and possibly run any programs installed on it?

In many cases, no. This is because most Windows applications load dynamic link library files, common files, system files, etc., in the Windows and Windows sub-directories. If they are stand-alone versions, it should run just fine since the programs requires only the files in the application folder to run...