I know I have done this before without any problems, but just to verify, I did it again. And it works for me.
Which JDBC driver version are you using? Mine is mysql-connector-java-5.0.4.jar.
Are you sure that you placed the jdbc jar in the right server/default/lib directory for the second server? I ask because I have often miscopied the file to some other directory (gee, you'd think it would work if I put in in deploy...)