NO
! It's TORQUE (at the wheels, NOT engine torque) and only TORQUE that determines acceleration. Unless you want to argue with Sir Isaac
!
F=ma
acceleration = Force (i.e. Torque) / Mass (i.e. mass of your car)
POWER is not something that is measured, only calculated. A dyno or rolling road is measuring TORQUE at various RPMs.
(assuming bhp and lbft units...)
POWER = (TORQUE * RPM ) / 5250
Look at ANY Power/Torque plot. POWER is always equal to TORQUE at 5250rpm for this reason.
BUT and it's a BIG BUTT... It's torque at the wheels that determines your acceleration and this takes into account the gearing between engine and wheels. So, an engine that can rev higher can still produce more torque at the wheels than an engine with more torque but lower RPM limit, since the gearing can be shorter to provide any given speed.
POWER can therefore be a useful indicator that an engine can rev, particularly if it doesn't have much torque (think vtec) and so benefit from shorter gearing providing greater acceleration.
How many tour-de-france cyclists do you see with big Arnie Swarzenegger legs... they don't have strong (i.e. TORQUEY) legs, but, they can peddle like the proverbial clappers (i.e. high RPM) and therefore use a lower gear and thus still have more TORQUE at the wheels.