I'd suggest that so long as you can't just lift it straight up without disconnecting the arm and turning it right around then it should be ok. It obviously works as it is but going any further will possibly require pulling the cover off, and that means dropping the coolant and taking out the pump impeller as well, plus the possible cost of a couple of gaskets.
It would give you a chance to clear the oil strainer etc but it's an added cost you may not want to deal with right now, and I understand that.
If the shaft is secure then don't worry about it too much. It might not be "ideal" but it doesn't seem to be going anywhere.