It depends on the horse. Remember, there's a massive difference in park-style/Saddleseat training and riding and jumping or dressage riding and training. Form and function can really feed off of each other. A horse bred like a park horse might look and move a lot less like a park horse if he's conditioned like a dressage horse. Conformation probably won't help you if you go for a very type-y park Morgan, but with basically good overall confo you shouldn't have any problems going through the motions with good riding/training. The biggest issue would be undoing or laying over any existing training or conditioning, but if they aren't started yet that shouldn't be a huge problem.
It depends on the specific horse and his/her personal attributes, but in general Morgans are amazingly versatile.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown