No, if Erwin were alive, Levi wouldn't behave like this at all. The reason Levi is being so stubborn is because he's the leader of his pack and he believes accepting his feelings for Eren will jeopardize their safety. Becoming the leader of his pack has left Levi feeling vulnerable and scared. He doesn't want to mess up in any way because he knows their lives are in his hands now. That's why he's being so careful right now.

And if Erwin were still alive and witnessed Levi's behavior, he'd know Levi is putting up a front. In fact, almost everyone in Levi's pack knows he's putting up a front because his feelings for Eren are obvious. He may think he's doing a good job hiding it, but he's not. It shows a lot more than he thinks.