Just make sure you have correct terminology and thought process:
A/P engaged and A/T connected...OK
A/P disengaged and A/T disconnected...OK
A/P disengaged and A/T switch selected on...NO
A/P disengaged and A/T DESELECTED (so in ARM)...WHY NOT (reversion mode in case PF stuffs up, for safety)
Yes G/A thrust (as well as FD guidance) provided after TOGA selected. 1 click 1000-2000fpm ROC, 2 clicks full G/A thrust...lots of grunt and lots of fun!