It all depends on the turn, generally speaking we design Emergency turns for speeds between 130-190KIAS, the radius of the turn obviously increases with speed.
Lets take Hong Kong for an example, the emergency turn starts after a 7nm straight ahead portion,followed by a 60 degree turn to fly down a wide valley.
If you accelerate to 210 KIAS in the straight ahead portion after taking off with a 10 kt tailwind, are you guaranteed that the radius of the turn will remain within the valley? The acceleration altitude shown on the takeoff chart is based upon obstacles used in the takeoff calculation, it is therefore worthless if you increase the radius of the turn.
We generally publish a limiting speed on the Emergency Turn, where possible, this speed will reflect the capabilities of the scheduled aircraft for that airport.
Therefore, it is NOT wise to accelerate before completing the turn.
Mutt