No. Quick-Tune is only available in the online 'events'.
It will be an important point in GT5 how they map out where you can and can't use setups. Hopefully time trials will be split into two - ones where setups are used and not used, and the leaderboard DB being able to show accordingly.
Quick tune is available for Arcade but only in the races, time-trials are not i believe, but it is available for drifting.
Correct me if i'm wrong, also not sure when it becomes available ( after which events i mean ).