Yes and no...
The motor doesn't "know" where the PWM is coming from, so yes you can control a DC motor if you can get PWM and no microcontroller.
However, there are some encoders (or at least encoder wheels) so the microcontroller can tell how fast and how far the motor has moved. Without the feedback the motors won't run at the same speed and it won't go straight.
...I don't see detailed specs, or schematic/wiring diagram, or example code so it looks like you're on your own getting that thing to work. In fact, don't see a complete encoder, just two encoder wheels.