I once grew Sweet Potatoes in a half bag of compost in my greenhouse - I suppose it was an 'average' summer and they produced lots of healthy looking foliage but very few tubers large enough to peel and eat.
I think the problem is that our summers are simply neither long nor sunny and warm enough for them to produce reliably - can't imagine that growing them outdoors up a trellis would overcome that.
Always worth a try though (especially if you've already bought them!)