I don't think so, once you turned off AVG's resident it should be fine. And the nice thing is the AVG spyware without resident is free for life (or until they decide to stop, I guess
). I tried AVG antispyware, it seemed OK, I still like my combo of Spybot and an occasional scan of Ad-Aware.
I guess the only issue you even possibly could have is if one or the other detected the protection database of the other, like how AV software will detect Panda AV's virus database as a virus since they didn't take measures to protect against that. But I've never heard of that happening with these two.