No, such a heat pump would not be wired using a cord and cap.
The justifications for using cords here are a) the need to service the equipment;
b) the desire to have a receptacle available to the serviceman; and,
c) 430.109(F) recognizes that motors might be cord and plug connected, without making any restrictions as to the conditions under which this may be done.
That last reference, to 430.109(F), is not as clear as it once was. Prior editions to the code clearly stated that such "shall be permitted." The closing reference to portable motors "under 1/3 hp" not needing a horsepower rated rated plug has been the basis for limiting application of the cord & plug as a disconnecting means has been used to justify limiting this method to small motors in practice.
So, out West, one will often find fixed appliances hooked up using cord & plug, especially when the appliance can be served by an 'ordinary' 120v/15a receptacle. We will use pigtails on dishwashers, disposals, trash compactors, air cleaners, air conditioning condensers, circulation pumps, and all manner of things that "back East" might be hard-wired.
Taking the word-wrangling out of the discussion, I like the cord connection mainly because it provides a simple and sure means of disconnecting what you're working on. No more hunting for breakers! It also recognizes that the 'other trade' is not likely to be there at the same time as I; I can provide the receptacle, and he can put in his stuff.
That said, even I have some issues with this cord & plug connected furnace: