Hi Jason, since SLAs are not applied by group, but rather are applied by impact/urgency/priority and by category, I dont believe this would be possible unless you create a condition and event to check for that condition - and one set for each group which would in turn fire off an SLA. It would be complex and being that it would have to be attached to every ticket, it would require a lot of overhead and would most likely bog down the system a lot.
Can you give us the bigger picture of what you are trying to do? It may be best to post an "idea" here for having SLAs be applied by Group.
Hope this helps,
Jon I.