Can whole-house fan can work in conjunction with a roof-mount power fan already installed on the roof years ago?

No. Whole-house fans cannot work in conjunction with roof-mount power fans.

The short answer is, No. Here's why. When whole-house fans run they pull outdoor, cool air through open windows into the living space (to cool the living space) and then push/dump any warm air from the living space into the attic. From there the whole-house fan uses all of the existing attic ventilation intake and exhaust vents as "exhaust outlets." To know if the whole-house fan has enough "exhaust outlets" it's necessary to know the Net Free Area of the existing attic ventilation intake and exhaust vents. Power fans do not have a Net Free Area rating. Only non-motorized vents have a Net Free Area rating. Thus, power fans are not a match for use with whole-house fans. Only non-motorized ridge vents, wind turbines, roof louvers, gable louvers are a match.