The bicycle is quite capable of acting as conveyance for a human (or perhaps bicycle peddling robot, or trained animal) in its current form, so that's an easy "no" from me.

As I said, if the thing can (i.e., without significant, non-trivial alterations to its current form) act as conveyance then it is a vehicle. It need not be in the act of conveyance, nor must it have an independent means of propulsion.

Edit: my simple rule breaks down when thinking about a flat piece of wood attached to rope. My mind says that's only a vehicle if someone chooses to use it as such for pulling objects or people. I'll leave the search for a universal maxim to others, it seems.

Belgian traffic code says "Het niet bereden rijwiel wordt niet als voertuig beschouwd.", i.e. "The bicycle that is not ridden is not regarded as a vehicle." When you walk next to your bicycle, you're effectively a pedestrian here. No idea how things are defined in other countries.

Interestingly, in Brazil's transit code a person carrying their bycicle unmounted is considered a pedestrian. Otherwise, they're a non motorized light vehicle.