I can say with confidence that the normal ethernet shield works fine with UDP. In one implementation, I'm currently using a Seeed Studios ethernet shield and a TP-Link TL-WR702N as wireless bridge (they call it a client, both terms work). The TP-Link "nano router" is a cheap and easy way to get an arduino device onto a wireless network. It also handles all of the wireless encryption for you, saving cycles on the arduino device. At about $31 for the seeed shield and $20 for the TP-Link, I am more than happy with the result. I send syslog data via UDP with that device all the time without any issues. Multiple arduinos close together could theoretically share a TP-Link router. I've no reason to believe that wouldn't work but I've not tested it.
FWIW, the Seeed studios version is a bit cheaper than the standard "official" ethernet shield. For the case mentioned above I didn't need the SD card slot that the official shield offers. The Seeed shield was about 65% of the cost of the official shield I own, and it's very high quality.