Ha! Hiring a MTB in Fuerteventura 16 years ago was a turning point in cycling for me. Started commuting by bike as soon as I got back. From memory it's fine, but you might need to get off and push for some bits and it's also worth asking at the hire shop about where you are/aren't allowed to ride. The sun will be strong, so cover up, and wear a hat and sun cream even if it feels cool. Take plenty of water and bear in mind that the cafes and shop will shut in the afternoon.
In case your Spanish is a bit rusty, it is effing windy. The yellow sand on the east of the island has blown across from the Sahara.
Good luck! Ride reports ----------------------->