Sorta-kinda. You most likely WILL get a connection, but there's more to it than that. The AirPort Express is a wireless router by itself, so it does all the functions of any other router along with providing wireless connections. This could be a problem, since one of those functions is called "Network Address Translation" or NAT. Two NAT devices (your wired router is just about guaranteed to be one) in a row spells trouble and confusion for most things beyond browsing. It's always best not to have to deal with that.
Further, you may want to share files and printers between wired and wireless computers, and just plugging the Express into the wired router won't do that; you'll wind up with two separate networks that won't see each other.
The solution is simple. When you configure the Express (using the AirPort Admin Utility), on the Network tab, simply UNCHECK the "share a single IP address" box. This turns the Express into a wireless access point, disables it's built in DHCP address server, and (as long as the wired router is running a DHCP server) automatically puts all wireless computers on the same network as your wired stuff.
Make sense?
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