".... am I correct in assuming that if he doesnt gait without a rider or in the pasture he can not be taught to do it?"
With the horse being a mix of the breeds mentioned, he may or may not naturally gait. There are gaited Curlies, but is my understanding they are a smaller percentage of all Curlies a nd Friesians aren't known for being a gaited breed. Floating regular gaits, yes, but not a foxtrot, running walk, or other traditional gaited gaits. The MFT in the horse may not be enough to bestow the fox trot..
That said, not all gaited breeds gait right off the bat. Some do from birth, but some need training to enhance the gait, or maturity to develop the muscles and movement for gaiting.
My horse, a Rocky Mountain, both gaits and trots freely in the pasture and some days he only trots while playing with his friends and you would swear he is not a gaited horse, however he only gaits under saddle and never trots.
Clear as mud, yah?