Can the 'Adafruit Non-Latching Mini Relay FeatherWing' be used with an Arduino microcontroller such as an Arduino Mega 2560?
Yes.

There's not a lot more to be said really.

It's a relay, and they provide a MOSFET and associated circuitry to drive it cleanly.

Just connect power and ground to the Arduino, along with the "Signal" pin to the GPIO pin of your choice, and away you go.

Note that the relay is a 3.3V relay, so you must power it by the 3.3V pin, not the 5V pin.