Yes, but keep in mind that it takes two clock pulses for nearly every divider/multiplier to calculate the incoming clock period that it's going to operate on. So if you're multiplying from a very divided-down pulse, well, it might take a hot minute for the multiplier to lock in. A much more sensible method would be to simply drive the multiplier from your 1:1 clock pulses.
Another pair of modules you might want a look at are 4ms's Quad Clock Divider and its expansion module. In this case, you have CV over your four clock divider/multipliers, so if you suddenly need a rapid-fire burst of pulses, you can simply send a CV (say, from a CV sequencer) at the right time to get that one output to jump way up in rate. Connect the same control signal so that it activates a start/stop on another sequencer, and there you are.
...and my calculator sits right to the left of my Push2. Welcome to the wonderful world of TIMING!