At least not in Hampton Fancher's original script.
Here's the climactic scene where Batty has chased Deckard through the Bradbury Hotel and Deckard -- after failing to jump across the roof to the next building -- is now holding on for dear life to a steel I-beam with one hand. Batty stands over him looking down, waiting for Deckard to fall ...
Deckard's hand is going. He knows it's over now, he bites the bullet of his anger.
He glares at Batty as his grip gives way.
Batty meets Deckard's angry eyes.
Deckard's hand continues to slip.
Batty is still looking at Deckard's rage. It moves the warrior in him, you can see Batty change his opinion.
Too late! Deckard's hand goes.
Batty's hand is like lightning. He catches Deckard's hand and holds Deckard.
Deckard's rage "moves the warrior" in Batty. He feels a kinship with Deckard, and so saves his life. It's an act of empathy. Batty has developed to the point a Nexus-6 test would fail to detect that he was a replicant.
That's the point.
This point would make no sense if they were both replicants.