It's to late to start charging membership fees. The sites already far to developed and set in it's ways to change. If they started charging members for usage this site would die.
But I do think you could make another site similar to this one and have it monetized. It's would just need to contain a different feel, layout, and you'd likely need relationship and dating specialists with validated credentials roaming the site offering an experienced take on the situation.
In any case, such a site wouldn't be GaG. It would feel different in almost every way and only be similar in contextual information. So to answer your question, yes I think less people would use GaG if it wasn't free.