it looks to me as though that is a dripless shaft coupling, as it is very different from the lock-nut type that prob came on the boat. have you ever looked in there when the boat is running with the boat in gear while the shaft is spinning? it should not drip at all if it is a packing free drip less coupling. (best viewed with two people, but can be done with one, make sure you are in the middle of the lake!) As far as taking on water, perhaps replacing the exhaust hoses will cure the prob, but there are really only a couple places where water can get in the hull:
Exhaust Hoses (as you are considering)
Shaft coupling (which you can view and see as described above)
Rudder port hole (someone would have really have to bang the rudder into something hard to scew up)
Propshaft Exit from boat (I think there is a seal there, not sure)
Sea Water strainer (if seal not on right or gasket not seated will leak like crazy)
Water pump gasket (would prob show as stains around water pump)
After you replace the exhaust hoses, launch boat, pull up all flooring, turn motor off, and sit look and listen for leaks or bubbles. (make sure stereo is off!) Sit for at least 10 min, any thing hull associated should show up by then.
If no leakage detected, start motor and idle until sure thermostat is open and watch sea water strainer, water pump & exhaust manifolds.
If still no leakage, put boat in gear and watch driveshaft coupling and look for any leakage there.
Thats about all I can think of for water entry and how I would test. Good luck and keep us posted, need to have you at the SE roundup!