In theory it would be great but in practice the bearing guide would blunt the blade and it would become pretty useless. Those saws you linked to are next to useless, they are a one use only then they generally break.
These types of blade are used for cutting stone out of the ground ,marble granite etc.
As the blade is running with the wheel no damage should occur to the tyres
I disagree. The 'teeth' on the blade won't land on the same spot on the wheel every time. It's not like a flat blade on a flat wheel where the teeth don't dig in.
I believe Pegas have recently started making scroll saw blade bands that fit on bandsaws. I don't know if they are here in the UK yet but if you have a look at the Feines Aus Wuppertal youtube channel, the guy on there is into all things Pegas and there are a few videos of him demonstrating a bandsaw with a thin scroll saw type band blade on it.
If these blades are available I think it could open up a whole new level of bandsaw box making!