No, they're not allowed on public roadways or bike/pedestrian paths. Which I think is fair and good, because they're not designed for either space.
There are a lot of different types of vehicles that aren't allowed on the roads of bike paths, but people still use them recreationally on private property. You can find retrofit kits to add the necessary mirrors and turn signals to many dirt bikes if you want to ride on the road.
If someone wants to ride on a bike path, they should have something that meets the definition of a bike. We've stretched the definition to include reasonable e-assist bikes, but we're not stretching it further to include everything with 2 wheels and a motor.
If someone wants to ride on the roads, they need turn signals and a mirror.
We don't have to allow everyone to ride everything on every public shared space.