If Barty had one day left to live:
Barty is one of those people who need a goal and a purpose to live. He is always, always, trying to be on people's good side, because he knows that for them to use him when they need him, he needs to be actually useful.
So when he gets the news, he feels like the chains are lifted. Sure, his life is determined by a purpose, probably not even his most of the time, but now? Now there is no 'life' anymore. Now he is free.
It's like the Aeolus' flask opened and everyone around it will be disoriented.
He has nothing to lose anymore, he just has one day. So he'd go on a revenge spree. Say the things he was always afraid to say, hurt people without caring about what they could do to him or his reputation, stuff like that...
At the end, he'd want to die in someone's arms. He'd try to contact his dad or his mom. He doesn't have a smooth relationship with them, but he still loves them. In case they don't reply or take him seriously, he'd seek out Evan. Barty needs him. Evan is part of Barty's identity, and he'd die relaxed in his arms.
Death doesn't scare him as much as he thought it would.... only the few agonizing minutes before midnight are torturous, but he did manage to ignore what waited at the end throughout the whole day.
Maybe that's what Barty is all about, ignoring what really matters for his own benefit and that includes his schedule death.