The ARD client is a normal part of Mac OS X and there is absolutely no harm in allowing it to be updated. You can hide any given update if you wish, but if Apple releases a further update, that one will then be offered and you'd have to hide the update again. I'd suggest you just let the ARD client update when an update is presented.
As long as you don't have Remote Management or any of the other settings turned on in the Sharing system preference, then there's almost zero chance that someone could be accessing your computer unless they had physical access to it to download some hidden control software or you were tricked into downloading and installing such software yourself.
As to the mail problems, I'd suggest you take that up in the Mac OS X forum. It's not connected with ARD, I can guarantee you. If you had someone connecting to your system via ARD, you'd see the cursor moving on the screen or would be locked out of your system.