Yeah, getting it to handle your Hotmail is super easy. Just make sure you synchronize the folders of your choosing (click on the parent "Hotmail" folder).
As for 'hiding' in the system taskbar and getting it off the main taskbar, I think you're out of luck. I've wanted to do the same thing for a long time.
Actually, I did have one a program that would allow you to choose what programs to hide -- worked rather well. But, I'm now on WindowsXP -- and they couldn't work together. So, if you're on something other than XP, you may want to look into WatchCat