In my experience, looking at a horse cross-eyed can make its back sore, so yes.
Specifically with what you're discussing, while I know horses and people are different, I would equate it to a person sitting back by arching their back rather than keeping a firm hold of the abdominal muscles and sitting more evenly on the seat. The horse's back may move, but is hollowed without support, and therefore has a good possibility of getting sore.
I think.. too much hand can make a horse' back sore, regardless whether too much leg or too little leg is involved. But again, a myriad of other things can make a horse' back sore. The rider position, the horse being asked to perform tasks he is not ready for, the horse is out of shape, etc etc etc.
In short, yes. But other things come into play including feet, footing, saddle fit. Look at the horse's muscling, especially neck. Is it correct? Sometimes if it's a young, green (or even older horse starting back to work) you'll get some soreness but this is usually alleviated very quickly by a day or two off. Continued soreness has a cause and usually it's not just one thing.