The two op amps in this circuit act as buffers. The first, the comparator, is a digital buffer. The second plays the role of an analog buffer.
It is always a good idea to buffer the input and output of your circuits, especially when you do not know what is going to be connected to them in terms of loads and impedances.
That's why any half decent guitar pedal must have buffers on their inputs and outputs.
Of course you can dispense with buffers if you know what you're doing. For instance, if you know that the output buffer of the gate is capable of driving the current necessary to charge C1 besides driving other circuits, you don't need the comparator. If you know that the input of the VCA or VCF is not going to unnecessary discharge C1, then off with the output buffer.
But I personally would not recommend it. The cool thing about analog synths is that you can patch together the various modules without having to worry about loads or impedance matching.
Good luck with your project.