Yes, you can also do that with REW, by measuring things like impulse response, but on the hardware side, you can look at the slew rate specs. Slew rate of modern electronics is generally a solved issue though.
Here's an easy to read an old article on Slew rate by Steve Munz of Audioholics.com, it included an Editorial by an
Electronics Designer for Classe :
Slew Rate in Audio Amplifiers - What Does it Mean?
With the Classe gear you are using, I highly doubt you have to worry about "the speed in which it takes to get there", you just have to make sure your amps have more than enough voltage and current your speakers need to get your the maximum SPL you need at you seats without clipping, or excessively high distortions+noise.