No. It entirely depends on how the tree is rooted.
The thing to understand is that rooting the tree is effectively setting the parent clade from which all subsequent "offspring" clades are derived. So ultimately the position of the bicycle it will depend on how the bicycle clade will be derived based on whatever traits are inherent in the rooted, parent clade.
This is why the use of a distinct, unambiguous outlier is used to root a tree, because otherwise the resulting tree makes little sense.
You're welcome to try if you want. I've provided the characteristic list I was using. Feel free to extend that list and see what results you come up with.
The software I used is Mesquite. You can download it here:
Mesquite - home
It actually does make sense when you consider how vehicles are categorized and which characteristics define those categories. In general, vehicle categories have to do with function, cargo capacity and weight, which tend to be a limited range of characteristics.
And while characteristics specific to those attributes will generally define that vehicle, things can still vary and some vehicles don't fit well into specific categories. Just consider vehicles like mini-trucks as an example:
Or odd vehicles like the Subaru BRAT. Is it a car? A pick-up truck? Something in between?
Then there are a whole range of characteristics completely independent of vehicle type. You could have a vehicle with 2 doors, forward engine compartment with a 6 cylinder engine, twin leather seats, SatNav system, stereo system with multiple speakers, side view mirrors, front headlamps and rear tail lights, and chrome wheels. These traits could equally apply to a sports car or a heavy duty Mack truck.
This whole discussion started from the idea that it was possible to create independent convergent phylogenetic trees of designed objects based on independent characteristics. But in practice, that just doesn't seem to be the case. Which makes sense considering that designed objects like vehicles aren't subject to hereditary constraints. Designers are free to create whatever they want with whatever characteristics they want. The same isn't true of biological organisms subject to natural evolution.