No don't think it can do layers. I tried again in fresh paint today but don't really get on with it that well I think the pressure sensitivity on the pen isn't set up right for me. I don't think there's a way to calibrate or change that yet though is there.
Try uninstalling and re-installing Fresh Paint. Before doing that, I found that I had to press way too hard, but this procedure seemed to fix the pressure response to a good degree. Someone else mentioned doing this and I thought I'd try it too.
Did this this evening on my SP3 in Photoshop CC. Playing with the brushes, I get on with this much better than Fresh paint, I had to use the Surface Hub to increase the sensitivity of the pen or I have to press really hard to get it to be visible. Much better after a tweak though.