The PWM frequency should be high enough that the motor's inductance has a smoothing effect, so current should not go to max as soon the PWM signal goes high. However the current will ramp up, so you should put plenty of capacitance across the power supply to reduce ripple (good ESC's already have low-ESR caps built in, but it doesn't hurt to add more externally). Most brushless ESC's run a PWM frequency of 8KHz or higher, which is fine for high inductance iron cored motors (coreless motors need 30KHz or higher).
If these two conditions are met then the power supply should 'see' a peak current only slightly higher than the average current draw, even if all PWM signals go high at the same time. Just make sure that the average current doesn't exceed 25A and you should be safe. If the motors experience heavy loading during start up or fast throttle changes then you may need to limit the throttle change rate and/or apply current limiting, to keep below the power supply's current limit.
The power absorbed by a propeller is proportional to rpm squared, so at low speed it will put much less load on the motor, eg. if the full throttle current draw was 7A then at 25% throttle it would drop to about 0.3 Amps. So long as your props are small enough to keep the full throttle current below 6.25A per motor you shouldn't have anything to worry about.
The oscilloscope picture below shows current flowing through the windings of a high power brushless motor at a PWM frequency of 12KHz. You can see the current ramping up to about 32A during the PWM ON time (full throttle current draw was 40A). Current at the power supply would have been much smoother than this, as I had several 220uF low-ESR caps across it.