You would think so, and it sometimes works, but I have had no end of problems. The procedure explained in DerfK's answer is correct. The most critical thing is to disable the DHCP server.
In a typical, cheap wireless router, the LAN ports are connected to a hardware switch, so traffic between LAN ports works perfectly. And the WiFi chipset is general-purpose and intended to be used to make an access point, so traffic between wireless devices works just fine.
The problems occur when wireless devices need to communicate with wired devices. This is implemented in software in the router's CPU, and that software was generally not designed to be used in this way. The most common problem I've seen is that DHCP requests from wireless devices are not relayed to wired devices. If your DHCP server is connected by wire, the setup simply won't work unless you use static IPs in all wireless devices. (This is particularly common with D-Link devices.)
I've also seen IPv6 just refuse to work between wired and wireless devices. (This one's common on Linksys.) And I've seen wireless devices refuse to communicate with wireless devices connected to another access point (where that access point is connected by a wire to one of the LAN ports).
One exception: If your wireless router can run OpenWRT, DD-WRT or a similar Linux-based alternative firmware, you should have no issues. And, of course, you may be one of the lucky ones and have a wireless router that "just works" this way.