Does Trackmania Turbo have online multiplayer?

I want to buy the Trackmania Turbo game to play online with friends, in much the same way you can in NFS or Driveclub. That is, I'd like to be able to create a party, join my friends, and race against them. Is this possible for this game on PS4?

Yes.

Trackmania Turbo offers local multiplayer (arcade modes and splitscreen) as well as online multiplayer on PS4.

In the main menu you can choose 'Online Racing', where you can use the 'Room Browser' to search for online rooms that are set to public by their hosts.

With 'Join a Friend' you can follow your online friends into a room they are currently playing in.

You can also create your own rooms and set it to private so only your friends can join your room.