No, I don't use Time Machine, but I do have both Macs connecting to the router wirelessly. Next time it happens I am going to make a point in checking to see if the iMac is maybe downloading something.
What's really weird about this MT is that it works 100% on the MacBook, but when I try it on the iMac it freezes up if I touch it with 3 or more fingers. So today I bought a new Bluetooth dongle, put it on the underside of my iMac keyboard and it began working perfectly. Yay! for about 5 minutes because as soon as I connected up the BT Mighty Mouse to the MacBook it started the 3 finger freeze again. Reverse the installations and everything is fine again, barring the occasional erratic tracking of the MT.
I have all the updates installed on both machines. Weeeeeird.