Yes and no. Heat pumps are available from several manufacturers that produce hot and chilled water rather than hot and cold air. These units can be connected to some types of hot water heating equipment. The limitation in the heating mode is temperature. Conventional hot water radiators and baseboard type elements are designed to operate at temperatures of 160°F and above (older systems as high as 200°F). Unitary heat pumps are limited to producing supply water temperatures of less than 120°F. As a result, on a retrofit basis (a home with existing hot water radiator or baseboard), the prospects are not favorable.
The best hot water system to connect to a GHP are radiant floor (or hydronic radiant slab) systems. This design, in which plastic tubing is installed in the floor slab as it is poured, operate at water temperatures typically much lower than radiator type systems. In order to minimize the required water temperature, the home should be well insulated and use minimal floor coverings. This type of system is more complex, in terms of equipment and controls than a standard water-to-air system and requires careful design.
In general, complete space cooling cannot be accomplished with a floor system since condensation would occur on the floor surface. As a result, this system generally must be coupled with some sort of fan coil unit to provide cooling and dehumidification.