Controlling multiple motor drivers with one Arduino
Yes.

using RC servo signals

This looks like it will work great with the DIP switches set to "servo" mode.
The documentation at that link implies that motor driver accepts 2 independent standard "R/C servo" inputs to drive 2 independent motors, and its output to those motors appears to be compatible with your 12 V 4 A DC motors (I'm assuming you have 2-wire DC motors, rather than 3-wire, 4-wire, or 5-wire motors).

The Arduino Servo library claims it can control 12 independent RC (hobby) servo motors on most Arduino boards, driving them from 12 independent digital output pins.

using analog 0 to 5 V signals

I'm not sure this will work for you with the DIP switches set to "analog" mode.
The Arduino analogWrite() library appears to only support controlling 6 independent motors on most Arduino boards.
As long as you are fine with independently controlling at most 6 motors per Arduino board, the "generate PWM and filter to get analog" approach looks like it would work just fine, also.

Related: Can Arduino Mega handle 6 motors independently