The big disqualifier is that MTB shifters won't fit on a road bike's drop bars.
Otherwise, as noted, the rear shifting will be fine as Shimano road and MTB rear derailleurs are interchangable.
The front shifting won't work well and if you fit a MTB front deraileur to the road bike, the cage curvature won't match the larger chainrings. It will work after a fashion but you will have to mount the fd too high and shifting will be poor.