Yes, because Custap Berry utilizes Priority and not the Speed stat. Priority will make sure you move first, no matter what. However, if your opponent uses a move of higher priority, they will move first.
A Custap Berry allows the holder to move first in its priority bracket when HP is below ¼. If the holder has Gluttony, then it eats its Custap Berry when its HP drops to ½ or below.
Move priority is not affected by Trick Room, which only reverses the Speed-resolved order of moves within a priority bracket; moves with higher priority are still performed before ones with lower priority. Some held items and Abilities also affect a move's resolution within its priority bracket (ignoring Trick Room), but not the priority itself.
Bulbapedia (Priority)
Bulbapedia (Custap Berry)
