Yes, it will. It looks to me like both The Bad Batch and The Mandalorian are following the Emperor clone narrative, Bad Batch from before his death and Mando after his death.
I didn't really see it as a twist. I assumed she was setting him up all along. Note in the beginning "recap" they repeated the line of having a special job for her. The Doctor was a loose end who could expose the Emperor cloning project, so she eliminated him. She's part of the group who are watching over the Emperor's clone, making sure nothing goes wrong.
Meanwhile, on Bad Batch, we're seeing the team who is working out how to clone him.
Hopefully, the cloning thing is a minor subplot in The Mandalorian. I'm FAR more interested in the recolonization and rebuilding of Mandalore that appears to be coming.

So there was a lot of speculation on sites that Bo Katan would be the villain of season 3, but it looks to me like the real villain is Paz Vizsla. I'm expecting him to challenge Din for the Darksabre again. Probably Din loses because he has such difficulty wielding it; then Bo Katan will challenge Vizsla and regain rightful ownership of the Darksabre. Then she will lead all of them back to Mandalore to reclaim and rebuild their world and culture.