It can happen. They can also wear out, so it could go either way at this point.
Easy enough to test though. If your reservoir is full and pointing the hose output down below the pump does not result in priming, then try holding it upright and dribbling some water down it to get to the pump from the other side.
Then hold your finger over the open end while pushing the button to see if that helps instigate something. Hopefully even a squirt in the face showing it's working!
Obviously this could be awkward, so a helper might come in handy. But if you're by yourself you can get a longer piece of hose for not too much money. But I think with the existing hose the dash switch can be reachable.
But speaking of the old hose, how old is it? If it's perfect, fine. But if it's questionable, I would replace it because little air leaks are going to make it a little bit harder to do the priming.
Of course, the real priming takes effect on the back side of the pump inside the reservoir, but some pressure buildup from the outside can really help. And air holes work against you.
Paul