Can't think of why there would be a problem within one EPO server - you can't move them between servers for many reasons, but between groups in EPO? No problems I can think of...
With 6.0.2 you could move machines between groups and the key information would be retained. There is logic built-in now that checks for the machine key association on every sync. If ePO is ever missing the key for a system, it will copy it from the system on its next sync. EEPC v6.1 also allows you to use the "transfer system" feature of ePO to move systems between ePO servers - in fact, this may have been in v6.0.2 as well. It would be worth a check.