Not true in my system. Imaging is spot-on.
It would indeed be more subtle than that.The dimple is a weak point that will succumb to flexure. The other issue will be dispersion. Think of how a phase plug or a waveguide changes the off axis response of a driver - same thing with a tweeter.
It is easy to show there will be a difference. For example, if your dimple is 1 cm deep right in the center of the tweeter then you will have quarter wavelength cancellation and a dip in the on axis response centered around 8500 Hz. This is probably not as bad as increased breakup or flexure though - as it may simply resonate/flex rather than behave as a piston and lose high frequency output/efficiency.
Remember that ring radiators do behave differently - so a dimpled tweeter will too.
Once you fix a soft dome then provided there is no permanent damage or crease then it should be as good as new (not unfortunately the case for a metal dome which will be toast)