What type of terrain makes an MTB mandatory?
I think you would find the bike handles reasonably on single track, 4x4 tracks and dirt paths but there are a few things to bear in mind.

I'd ride single track but stick to trails graded easy.

Where an MTB would be mandatory would be anything above that. The following features would require a MTB (or at least no gear or being on a short ride ie. mud).


Gradient (up) - fine on a short ride, horrible on a long ride carrying gear.
Drops and Jumps - wrong bike type and not worth risking damage.
Rocks and Roots - you could do it but wrong bike type and not worth risking damage.
Switchbacks - more difficult when on a loaded bike.
Mud - infinitely more annoying when you can't have a shower at the end of a ride, worse if the options days away.
Gradient (down) - what impact will extra weight have on your brakes.


Upgrades wide to handle more off road riding I'd look at disc brakes and 32mm + cross tyres. Play with pressure until your happy.