So after reading what you just wrote, I've had a thought. That's was a master-class play on Dany's part right there. Have an uncomfortable conversation with one person, who is both inconsequential and invaluable to your political influence at the same time. While Varys has a large network and vast immediate and potential knowledge, he could theoretically be replaced (i.e. Qyburn and Cersi). Correct me if I'm wrong, but all of Dany's "court" were present for the conversation with Varys.

If you scare him off or don't get a favorable response, then you show the others the consequences of betrayal. If he stays (swears fealty), you show the others that mercy is earned, not given freely. It almost seems like she knew what Varys would say two steps ahead. While she may not have gained any true allegiance with Varys, the others think that she has. And that is valuable in itself, even without the possibility that she did actually earn Varys's trust.

I'm curious to see what happens when Varys learns that Littlefingger is at King Snow's court. I hope that comes up.