Possible? Yes. Practical? Sort of. Win98 is mediocre at best in terms of networking, and you'll have your hands full finding a decent wireless anything for it. But if you just want to wire it to the AEBS, yes, you can do that without too much trouble. You'll need the Win98 disc and some fortitude. Oh, and it works much better with Windows 98 SE, so if that's what you have, you're a step ahead.
Here's a nice, step-by-step procedure to set up networking on a Win98 machine from Ball State University. Depending on how your AEBS is configured, the IP address mentioned in the last step may or may not be as indicated.
One more thing: it may be more effective and less hassle for you to just buy a new WinXP computer (and keep all the other stuff like keyboard, mouse and monitor) because XP handles networking without any extra work, and is overall a better OS by far than 98.