What are these metal ducts/tubes going into the attic used for?
Assuming your water heater is gas, those tubes are likely providing ventilation for the gas burner that heats your water.  If so, they should not be filled in, they were most likely deliberately added when the water heater was boxed in.  

If you DO want to close them up, replace the door on your closet with a louvered door that have the louvers permanently open.

As for efficiency - the room for the water heater is closed up - so no, the efficiency loss is minimal.