Yes.
Which OS X version will depend on which G3 PowerBook model that you have.
The main difference is the ports that are available.
Does your PowerBook have USB ports, and do you also have FireWire ports?
A couple of models have none, one has USB added, and the last G3 PowerBook has both USB and FireWire ports. The oldest model cannot easily run OS X at all. The last G3 PowerBook can be upgraded to OS X 10.4.11
Then you have either the model called 'Wallstreet", or "PDQ"
The newest OS X version for you will be OS X 10.2.8
If you really have 32MB of RAM memory, then an OS X upgrade is not possible until you upgrade to at least 128MB. Your PowerBook can be upgraded to as much as 512MB.
I will guess that you will be limited to only a couple of wireless cards that would either be supported natively by 10.2.8, or have drivers for that version of OS X.
"Supported by OS X" is not the same as "supported by OS X 10.2", so you will need to do your homework before you buy, or talk to the tech support folks at a site that supports Apple and OS X, such as OWC (www.macsales.com)
Here's one, for example, that needs OS X 10.3 or higher (so likely would not work for you) http://eshop.macsales.com/item/Edimax/EW7708PN/
Mac OS X 10.2 (or any Mac OS X that works with 128 MB of RAM) is painfully slow, even in newer hardware. So max out RAM - or as an alternative for a newer OS perhaps some of the PPC-supporting Linux distros might be an option too.