Turbo props do have a lag. I don't have exact number, but it seems a TF run about 6-7 seconds to full throttle, recips props are under 3 seconds, and a turbo prop should fall in between there. However, the question shouldn't be how fast it is to 100% to how fast it can go from slow and level power setting, to a slow and rapid climb. Turbofan airliners tend to have pretty high thrust to weight ratios at low altitude since the engines have to be oversized to operate at high altitude. That is to say, 30% of available thrust on a 737 is probably more than the P-3 could produce in it's glory days.
Should also mention that 737s have big spoilers. Cary spoilers and a bit of extra thrust, then just drop the spoilers when you need to climb. Instant gratification.
BTW, there probably are good reasons the A-10 didn't use turboprops.
Or the S-3, for that matter, which used the same engines as the A-10.
It's important to remember that, on a turbo like a P-3, the "instant response" so bandied about comes NOT from the engine being able to spool up fast, but from the fact that the thrust produced is caused by the prop BLADE ANGLE. The engines themselves only have two settings...high and low RPM. The power levers control prop pitch. Changing that pitch changes thrust.