There is a pump that circulates water from the tub through the coils of the exchanger. 

We also discovered that the amount of items moved into common areas on the property (garage, backyard, basement and entry ways) had grown to the point where access to the electrical panel was obstructed, flammable items (i.e. open coil heater and mattress) were in the vicinity of the furnace and water heater and a garage that was barely standing was packed.

I also say that if the air handler coil starts getting dirty I will know they have been negligent and that they may be paying for a coil cleaning.  

We also had one where the evap coil was literally coated in nicotine so was not performing effectively.

It appears besides popping out and cleaning out the washable filters there are additional recommended maintenance in cleaning the coils and blow wheel etc. every so often.  

I won't be able to get a brad nailer behind the HWH or toilet after they are installed so I'll have to do it while I have the chance.

It's adding A-coil, line-set, condenser, wiring for it all, done.

It appears they installed the new coil on top of the old furnace air handler and blower.  

The house has ducts for a heater but does not have a condenser and coil.

I just had to replace an electric glasstop stove recently, and decided to spend less for the rental property and go with coil burner type than another glasstop.