If I have my desktop connected to the wireless router, and want to print from my laptop, does the laptop need to have the printer driver installed as well for my printer? I would think that since the desktop is handling the task, the laptop wouldn't need it. Is this accurate?

Lots of stuff is confusing in this post. Digested.:

Are the following true?
1. Desktop connected wired to wireless router.
2. Printer connected to desktop (not a wireless printer)
3. Laptop connected wirelessly
4. They all are on the same workgroup. (Default is WORKGROUP)
5. Printer sharing is turned on.
6. Printer driver is installed on laptop
7. Desktop is turned on when trying to print.

No, the drivers are still required. However, you don't need to install them directly. When you go to Add Printer, and find it on the network, it automatically sucks the drivers from the other machine. When you install the drivers on the host machine, you can include drivers for other operating systems, that is so if you want to network with linux, or other versions of windows, or even mac, it can still suck the drivers onto that machine without having to down/upload them onto that machine via other options.

Your print request is not processed by the host computer. The spooler on their machine is never accessed. It just opens up a sort of virtual port to the printer.