I received the following response from Cypress Technical Support:
Yes, the reason we suggest HW Analog mux is switching speed and hardware control.
Yes, you can use Analog Mux. It is equally good as Hardware Mux if you are stopping ADC conversion before switching and restarting after switching.
Just remember to account for settling time.
I see a lot of customers trying to do back-to-back conversions without allowing for some settling time after switching inputs.
This is particularly important if you use hardware SOC (Start of Conversion), as you first sample after
switching inputs may be noisy...