Our SOP is to accelerate at the acceleration altitude, usually 1000' aal, regardless. If it's during the turn, before the turn or after the turn it doesn't matter.
The emergency turn is designed to take you away from any high ground and keep you within a safe part of sky. Therefore, if you are visual or under radar control (vectors can be requested as long as you are above the minimum radar vectoring altitude) you may ignore the emergency turn.