[Frenchgeek]

Only if you forget to fold it back before driving.

[Kirby64]

The solar panels merely existing on the top of the roof are probably enough to offset the additional power gained while sitting still. The drag from a little cargo carrier on top of a Tesla is significant.

[jebarker]

I often see people where I live choosing smaller more fuel efficient vehicles and then permanently keeping a storage box on top. I always wonder if the drag offsets the gas savings.

[fy20]

I drove across Europe a few months ago with a bike on my roof, and I was consuming around 10% more fuel. I'd say it's likely your theory is correct.