You are correct that using an attic fan is generally a lousy way to cool your attic when you have a central air conditioning system. And, you are also correct that the reason is that it will not only suck hot attic air out, but the attic fan will also suck out the air-conditioned air from inside your house. Using passive ridge and soffit venting for attic ventilation is a better idea.
For the most effective attic ventilation, I recommend continuous soffit and ridge vents. Air will enter the attic at the ridge, run up under the roof sheathing where it carts heat away in summer and moisture away in winter, and exit at the ridge. This 24/7 attic ventilation solution is far more effective than any other type of mechanical or passive ventilation solution.
However, to answer your question, having ONLY a ridge vent for attic ventilation will not work. To have an effective attic ventilation system, air must be able to enter at the soffit, travel up under the roof sheathing (removing heat in the summer and moisture in the winter) and exit at the ridge vent. If you only have soffit vents, it won't work.
Once you have a properly functioning soffit and ridge attic ventilation system, you can shut down the attic fan for good!