Yes!
You can configure your input device via the out of game options.
Phantasy Star Universe™ is capable of supporting a wide array of USB input devices, including popular ones such as:
Dual Shock 2, 3, and 4, as well as the Duel Sense
Xbox, Xbox 360, Xbox One
If you're having trouble with the game not detecting your controller, then you may need to set your controller as the preferred device.
You can do this by following these steps (Windows Only):
Open the Run Prompt (Windows Key + R)
Enter the command joy.cpl and press OK
In the Game Controllers window, press the Advanced... button
In the Preferred device list, select your controller and then press OK