very likely imho. they do feel slighted by the mc and he made sure that the phoenix binds to the daughter, which also throws a wrench into their plans. her treatment should get at least a bit better due to her contract with the phoenix, but they still won't turn into a loving family suddenly, so hopefully she will be able to exit the family sooner rather than later. they probably want to keep the phoenix within the household though, so her engagement will likely be canceled.
The Household is kind-off stuck now.
They can't continue with that girl's marriage as it would mean that they would lose the Pheonix. But surely that 40+ year old guy wouldn't easily leave the chance of getting a bonus like a Pheonix either and would surely try something.
But that Household can't easily keep her locked to the family either as the other strong family including the Royal family would try to get there hands on her in some way.
The only way they could keep her restricted to the Household is by declaring her to be the next Heir.
They can't even easily suppress or mistreat her easily now, as if any other stronger Household gets the news about it, they would use that as an excuse to take her away from them.
Also the Royal family probably already knows that MC is the one who summoned the Red Dragon (if that doctor can spill the beans on him to that family, he can do it to others as well).
So, MC can easily make a deal with them by giving them a summoned beast in favour of helping that girl (or atleast make a situation were they don't bother or allow anyone to force her out of decision she makes herself).