It's definitely possible. I'm doing the same thing, except i monitor light and temperature sensors and send back an xml document with each reading over a socket to a program running on a pc that parses it and stores it into mySQL.
I ran into a few problems along the way though. I got answers here on the forum.
The first is that strings take up a lot of memory and writing out XML tags uses a lot of strings. You have to push them into program memory. Check out this post on how to do this.
Once I did this, it started working better, but would still hang after a few connections. I found this post about a bug in the Client class. I just made this change to the library and will test it tomorrow, but it seems like a fix to my problem.
http://www.arduino.cc/cgi-bin/yabb2/YaBB.pl?num=1227735530/5
Memory, again, is a big issue. With the Ethernet library added in, your at about 13k with very little code. So, you don't have much room to work in and who knows how much RAM this eats up.
Michael