Hybrid platforms composed of a floating offshore wind turbine (FOWT) and wave energy converters (WECs) may possibly reduce the levelised cost of energy of both energy harvesting devices and improve the platform dynamics. This paper investigates the dynamics of a hybrid platform composed of a semi-submersible FOWT combined with three spherical heaving point absorbers (PAs), either floating or submerged, under turbulent wind and irregular waves conditions. Since the WECs are attached to the floating structure, complex hydrodynamic couplings occur between the floating bodies. In this regard, a parametric investigation of the power-take-off system is performed to understand the wave power absorption and motion characteristics, which are compared against their respective stand-alone configurations. At sea states with short wave peak period, both hybrid platforms (with floating or submerged PAs) were able to operate under maximum wave power absorption condition and extract nearly the same amount of wave energy as the PAs attached to the ground (stand-alone), while providing the additional benefit of reducing the horizontal nacelle accelerations of the FOWT. On the other hand, when operating at sea states with long wave periods, the hybrid platforms may need to restrict the wave power absorption capability to prevent additional nacelle horizontal acceleration.