Yes, you can indeed run Sun Java 1.5.0 under Ubuntu 7.04 just fine.
That is what my Linux box uses. I suggest uninstalling all other Sun Java versions, keeping *only* the one you intend to use. The Wiki instructions were recently updated as I was testing with Ubuntu 7.04, so they really should work for you, too.
My Linux box is hardwired to my home network, so no wireless setup to worry about there for me.
Jonathan