Yes, it will work.
It looks like you may have to use the original DocReader (
http://www.freewarepalm.com/utilities/docreader.shtml), but if by any chance this device has been upgraded to OS 2.0, I'd recommend CSpotRun (
http://www.32768.com/bill/palmos/cspotrun/).
Whatever you do, I hope you're not paying much more than $5 for this Palm. A Palm III, which will have four times the memory and a backlight, as well as run better readers like TealDoc and iSilo, will run ~$10 on eBay.
Also, if you don't have a computer with an old-fashioned serial port, you'll have to buy a separate USB adapter (another $20) to get files onto the device, in which case you might be better off looking for a first or second-generation Handspring Visor (just a little more expensive than a Palm III, but shipped with USB).
Good luck!
Curt