If the game is not supported, then yeah. That cold be the problem. The wheel may still function but not to a great degree of success.
I use a Thrustmaster now, as the PS4 was not compatible with my older Logitech wheel.
When I start the PS4, I log into my PSN Account with a controller with the X button.
To get the wheel working, I simply return to the log in screen and press the X on the wheel, the wheel is now a second controller on that PSN Account.
I assume the Logitech wheel connects in the same way, that will be the case for any additional controller/wheel you are adding.
A Firmware update might help, just connect the wheel to a computer/Laptop and enter the Logitech web site and upload the latest Firmware.
Considering these wheels are considered to be compatible to the PS4, the Devs are not making it easy by shutting out some wheel producers to their games.