Yes, but what is the point? Well, creating Drama, I suppose. But apart from that. Neither of them is particularly likeable (I know, I shouldn’t expect it, this is a soap after all) and I find myself entirely uninvested in which of them “wins”, or even in whether they can achieve a working accommodation.
You could make this slightly more interesting by having them trapped in close quarters (say, in a hut surrounded by zombies) and having to work together to survive. But not much.