See I just don't see Mace coming down himself. In the epilogue at the Small Council meeting Mace had declared he would march down after the trials. And at the conclusion of book Kevan who was Regent is murdered. Kevan's death will usher in a dilemma, who becomes regent? Mace will likely want to place himself in that position and name someone else Hand, this will all look suspicious especially by Cersei. She may have command over the Lannister forces or at least she has Ser Robert. There will be such distrust among the Lannister and Tyrell forces inside the city. Everyone in the Red Keep will be alarmed and on high alert. Such a serious matter would probably keep Mace from leaving King's Landing since he will have to deal with the investigation of Kevan's murder and the trials.
Varys killed Kevan so that chaos and disorder would continue to preoccupy the Crown's time and hinder their response to Aegon. So I think Aegon will decide to march on KL and may succeed. He has momentum and forces, he has Varys, and Arianne is about to show up to possibly declare Dorne's allegiance. I think Aegon may sit on the Throne next but he's definitely not going to be the last.
Although I don't know if Aegon or Connington know about Varys.