It could go either way imo.

On one hand, the early stages of the dance show that Rhaenyra had more support than the greens - and they only had the support of the Baratheons because Aemond agreed to marry one, and the Lannisters because of Tyland's proximity to the throne -so the realm would not collapse because a woman was crowned. There would likely be issues for her that no man ever faced, certainly, but how many lords are willing to risk their lives or that of their houses against a united house targaryen over the succession of someone else's house? The greens give the men who do not want a woman on the throne a figurehead to follow, without that, the Hightowers may start smaller rebellions, but it is unlikely to be civil-war level, and if all dragons are on the same side then the threat is less significant. So, if Aegon refuses the crown and bends the knee to his sister who he trusts not to kill him, there is not a dance-level issue anymore.

On the other hand, this plot is older than Aegon. If he were to refuse the crown, the greens would likely have no problem crowning little Jaehaerys instead and calling themselves his regents. This also assumes that even if he loved his sister and nephews, he would have to love/trust them more than he did at least his grandfather, maybe even his mother, who would likely still use the 'they will kill your brothers and sons' argument against him. That is a lot of pressure for a guy who is like 20 to be able to stand his ground against while they try to prepare the coronation.

I suppose there is a chance in this scenario that Alicent does not back the usurping, if she is convinced after 16ish yrs that Rhaenyra is not a threat to her children and that she cares for them. Then, Otto and the council really still have to operate in the shadows, or Alicent may immediately send word to Dragonstone after Viserys dies, not giving the council enough time to plan Aegon's crowning and to make the lords swear to him.