If you want something like that online, you'd have to know how much time it would take to make it possible, then it would depends on the drivers skills, letting themselves pass without blocking, keeping their lines, how fast they can push each cars they have, etc...
If you end up in a terrible lobby, it would suddenly look like an A-Spec time trial where the AI is moving all over the track not really knowing what they're supposed to do, except that it would be actual people moving all over the place which would be like someone said above, a "crash fest ramming to the finish line" or something of that sort, I really wouldn't enjoy it.