I was watching a documentary about Lincoln on the History channel recently and they discussed the possibility. While Lincoln was on the road, he often invited some of his soldiers to sleep in the same bed with him.
However, the narrator also pointed out that many people sleeping in the same bed was a common occurrence back in those days. Rather than having sex on their minds, it was more likely that they were thinking about the pure, unadulterated, idea of the comfort that comes from sleeping in a real bed rather than on the ground or in a tent.