No, not in a wireless sense. The only certain way to "extend" your existing router's range is to connect it to the Express with an Ethernet cable:
The "extend a wireless network" option applies only to Apple AirPort base stations. It will not work with other routers.
I believe you may be able to use WDS with the Linksys WRT54G but it is certain to be an exercise in frustration, even if you get it working properly.
This may interest you: http://hints.macworld.com/article.php?story=20060609053254368
Read it only if you are a glutton for punishment, or simply a nerd (same thing).