No. Rumor is if you remove the muffler or put on a tray, you might be able to fit a spare.
The location of the spare is something I have been thinking about. But each time I come back to, that it's not really a hindrance. If you are carrying a ton of wood, then take it out and throw on the roof. If you find that you will need the bed space everyday, get a trailer hitch spare tire swing. Popular here in states on the Toyota. If you are using it for touring, then it sitting in tub does not eat into tub space ro much.