He could tell her she wasn't dreaming all he wanted- the problem was, in her current state, there simply was no way to prove otherwise. Claire was on the edge of fucking fainting, just by turning the idea that Castiel had fathered this... being in front of her...around in her head. Add to it the notion of Dean and Sam raising him?
Claire didn't even look at the phone. She just shook her head, as if that would wake her up.
"No- Cass would've said something," she almost growled, gritting the words through her teeth. "This isn't real. He would've told me I had a fucking half brother..."