I'd say not. If it's trapped in a cavity in the pad, the grease cannot spread out and form an even, thin, layer. It may prevent even pressure on the pad.
If whatever heatsink attachment is suitable and insulation is not required, I'd remove the pad completely and only use the thermal paste.
It should work far better anyway, as thermal paste / heatsink compound is only supposed to fill the microscopic imperfections in the surfaces, to avoid insulating air pockets when the two items are clamped together.
Thermal pads are always less effective than that; but more convenient and mechanically less critical.