Wirelessly posted (iPhone 4: Mozilla/5.0 (iPhone; U; CPU iPhone OS 4_2_1 like Mac OS X; en-us) AppleWebKit/533.17.9 (KHTML, like Gecko) Version/5.0.2 Mobile/8C148 Safari/6533.18.5)
Yes, you can definitely use an airport express for that purpose: you set it to join a wireless network and then set the checkbox to allow Ethernet clients.
You can then plug your computer into the Ethernet port and it should work fine.