Would a clogged drain hose be enough to cause the system not to pull the moisture from the air?
It could but I would expect that the drip tray that runs around the bottom outside of your A coil would overflow and you would see water dripping out of the furnace somewhere. But this would depend on you set up.
The reason I say this is that the surface area of the water in the drip tray is fairly small so I do not think that the air going through the system would be able to pick up enough moisture to keep the humidity that high. But stranger things have happened.
Open the system up so you can check you A coil and the drip tray.
there is a possibility that the underside of the A coil is so dirty that it is holding the moisture and not letting it drain off.