Well, just for giggles I went ahead and tried this on my setup.
A) I removed the Wyze Chime controller and didn’t hook up the Chime at all.
Everything was normal. The Doorbell module seemed quite content.
B) I connected the wiring directly to the Chime (mine is digital).
Doorbell is now unhappy making buzzing and popping noises.
I quickly pulled the wire off of the doorbell and everything is back to normal.
So, at least with my Digital doorbell, this is not a working configuration.