Some things you should know.
First, you called it about the 4 channel motor controller. Arduino pins, on their own, can not provide the power needed to run motors. The Arduino sends the control commands to a motor controller, which is connected to the motors, and a power source and THAT combination provides the power to the motors.
You specifically asked about an Uno being compatible. The answer is "Maybe."
There are three versions of the Rover 5 and the one with 4 motors also has 4 encoders. The encoders provide pulses that can be monitored by a microcontroller and translated to provide motor direction and speed information about the motors. You’ve probably noticed that you have a lot of pins on the Rover 5. You have 4 red, and 4 black that provide power to the motors, and then you have 4 sets of red, black, yellow, and white. The red and black provide power to the encoders, and the yellow and white are the outputs of the encoders.
You do not specifically need the 4 channel controller, but it’s the only device I’m aware of that provides a space to connect to everything that comes out of a Rover 5. You’ll still need an Arduino (or other controller.) to monitor and control the Rover 5.
You do not need to connect the encoders to get the Rover 5 to work, and indeed, with an Arduino Uno, you do not have enough pins to monitor everything independently.
Here is an earlier post that describes the various ways a Rover 5 can be controlled via an Arduino, and what pins you would need to connect everything.
https://www.robotshop.com/letsmakerobots/node/26777
Basically, you need an Arduino Mega, to provide all the pins.
A better way is to get something called a “Red Back Spider Controller” which is basically an Arduino Mega, work-alike, with an integrated power supply, and pins, rather than the sockets that you’ll find on a Mega.
If you don’t connect the encoders, you can run the Rover 5 with an Arduino Uno, but you’ll still need a motor controller/driver. The Dagu 4 channel controller, is reasonably priced and will allow you to integrate the encoders later.