Shouldn't be any problem, anything on the network will communicate.
Even the cheapest wireless routers have a few wired connections. I just got a Netgear MR814 router for $20 AR from Circuit City. It is just an 802.11b unit but it has logging, a real firewall and plenty of configuration options. I went with a USB adapter for my desktop system so I could easily swap it if I moved stuff around.
You should be able to get a router and an adapter for under $50 net.