No, because they don't use drivers in DOS. You just need to plug it in, install any drivers for the card you have installed, and then it will work right off the bat. Make sure the system is OFF when plugging the stick in, otherwise you can damage both the joystick and the card irreparably.
As I told you, grab a copy of Commander Keen 4 and test it out there. That game is known to work with that stick. Use the AWE64 too, that's the closest to my AWE32 which likes that stick. You can also try a M/I/O card, but most of them are ISA or VLB as all the PCI systems had onboard stuff.
If the values check out in the stick with a meter (Check to a varying resistance on the pots, and continuity on and off for the buttons.) when measured from the connector, then the stick is 100% fine. There are no real electronics to go wrong it it, it's all mechanical with the exception of pots and simple buttons.
Also try another stick if you have it on the cards.