It will really be a defining moment for her: Show she really does adhere to the laws of succession and step aside for Aegon, or show that she really is just a hypocrite and try to fight him.
She is going to want to meet him, and the meeting is going to set the stage of their relationship. Is he going to come at her making demands, "making a claim", or is he going to be coming at her as a junior partner, or offering an equal marriage. If he tries to be overbearing or boss her around, she's not going to care who he is, legal claim or not. They're her dragons and her Army. She'll tell Aegon to take his primogeniture legal claim and shove it.
I don't think he's going to do that. I think he wants to woo her. He knows he's not going to get anywhere telling the mother of dragons and sacker of cities: "hey, you belong to me now, and the IT is mine too, give me your dragons".