I agree to a point.
Here are the regs so it clears up the grey area for you…
“Antlerless deer must be harvested and tagged before a buck to make the buck legal.”
So, yes, you should get down and tag it, but there would be no reason to gut or drag it out if you didn’t want to.
The rule makes sense since you need to confirm that the doe is actually down and recoverable before you can shoot the buck. It would suck to have the doe run off the property, shoot a buck, then be SOL with an illegal buck and no doe.
edit – if she falls within sight and is obviously dead, I’m sure it would be awefully tempting to just leave it lay and keep hunting. On the off chance that a DNR officer happens to be watching, though, they may dispute the legality of any harvested buck if the doe isn’t tagged first, even though it might seem like a trivial point. I’d wouldn’t take the chance and tag it first.