I'm one of the Linesmen for the Spanish sections, the other is a Spanish guy called Isaac Felui. Our role is to check and collate the trails that have been submitted by volunteers or found on Wikiloc, etc. so we don't know all of the route personally - yet!
Regarding your question, bearing in mind that in Spain there's an almost universal rule that a trail has to be 4 metres wide to be translatable by motors in theory you are OK. But in practice many of the trails have very poor surfaces including deep rights, washes and are sometimes more or less blocked by boulders - these also change constantly due to the extreme climate here so it's ver hard to be specific.
I'd say that if you're proficient on your big bikes then you'd be OK, but that all depends on how loaded your bike is. The handful of people who have done the Pyrenean sections have had some problems with heavily laden bikes, no matter large or small.
The good news is that hotel accommodation is plentiful and cheap - almost all camp sites will be closed from this weekend until next Easter - and you don't have to book/check-in early. There's lots of info about this on my web age but I'm reviewing and updating all of this at the moment so follow it for updates.
Regs
Simon