Hello VegasGrace,
I have two Carrier PTAC units we installed in add-on sunrooms (one built specially for the dogs, but that is another story
). Anyhow I am not familiar with that brand but can give you some insight into PTAC units in general.
Pros:
1. With the heat pump configuration you can remove the need for the baseboard heaters.
2. Since you will have multiple units you can easily control heat and cool in various sections of the home.
3. When a unit requires replacement you can replace just one and not a whole, or major parts of, a fully ducted system.
Cons:
1. For each unit you put in you will most likely require separate 240V electrical runs which will also mean having space in the main breaker distribution box, an electricians time and the cost of additional hardware, cables, etc.
2. By running PTAC units you can save some on your electric bills by controlling sections of your home but if you have a family that is out the window. Even with a heat pump these units will consume a large amount of electricity handling a whole home.
3. You will need to create appropriate sized openings in walls and properly brace them when installed. These can easily span across, and through, stud bays and will require additional bracing be added to make up for the lost studs.
4. Even the best units have the potential for leakage from rain entering the casing from the outside. Our sunrooms are designed to handle any of this leakage and it is visible when it happens. In your situation you can have leakage go undetected for long periods. Remember that hotels and motels usually have overhangs that protect these from rain, for the most part.
5. Because of the way they operate there will be air infiltration through the units casing and components which can affect your operation (make it run longer, harder) and affect your electric bill. You will hear that these units are "Very well sealed". Fact is the seals are like anything else and wil degrade over time.
6. Because they are required to be exposed on the exterior side, to allow the coils to perform their job, they will require more maintenance in the form of cleaning regularly. I see you are in Vegas? I'm sure you have dusty conditions there and the coils will need to be cleaned more often. Keep in mind that you will have to be careful if you hose them down as you do not want to cause water damage to the home through the openings. Along with this the exterior casings are generally not screened and you can easily have bees, wasps, etc., building nests in there.
7. The interior filters on the unit will also require more attention than a standard ducted system. These filters can become dirty and clogged quickly, they are not meant to be left, in your configuration, for a month at a time.
I see the unit you are looking at appears to be an Amana unit. Depending on your heating and cooling needs these can run you up to $3200 just for the units themselves (based on one for each you now have). Add into that the cost of the electrical discussed before, the extra labor to create the openings, the cost of the labor to install them, etc., etc. and you start reaching a pricey solution.
These units are good for their intended use which is mostly small hotel rooms, small additions (like mine) and very small residences when one or two would suffice. I would expect with four window units now you most likely have a smaller home, one story, etc. Have you looked into the cost of adding central heat and air? You can obtain packaged units where everything is located outside the home and ducted into the home and through the attic, if attic access and space does not allow installation there.