Yes. Garden rooms are a common use case because they can heat up quickly in sun and cool down rapidly in winter. A reversible air-conditioning system can provide both cooling and heating without needing to extend the house's wet central-heating pipework.
Capacity should be based on the garden room's insulation, glazing, orientation, size and how it is used. A highly glazed room can have much higher cooling demand than another room with the same floor area.
Doherty's Glasgow air-conditioning service includes garden rooms. A survey can confirm the unit size, external position, electrical supply and condensate route before the internal finish is disturbed.
