I think there is a certain amount of chemistry between Kate and Alex, but possibly not enough to overcome the problem that they don't like each other.

However, I am grateful for the sequence, because I hadn't picked up on the little grin that Alex made after he had put a stop to Kate and Spencer's Orange-juggling game. It just went to show what a petty little tyrant he can be, given the chance. And it also indicates to me that when Alex assembled his harem on the rich side, he chose the other three because Kate is not the type to be controlled by him.