I suggest we just forget about the usefulness of this question in any serious flying context.. I've flown once with a directional gyro failure. At this time, I had no idea about compass errors but that did not stop me from navigating precisely with it.
I thought that the error was linked to the mass (compensating the dip) lagging behind the axis, isn't it?
I read your post in the linked topic, and you raised a good point : if there was no dip compensating mass, but just a mass well below the C of G, then you're right, the compass will have an "attitude angle" and dip towards the pole, hence the C of G will no longer be on the axis, hence turning/acceleration errors.
However with a non dip compensated compass, these errors should be inferior to those of a dip compensated one ? (this is suggested by Gil Stone's post but rephrased)
And finally Gil Stone tells us that some compasses will use both solutions : pendular design + a supplementary small weight to optimize the compass for a certain latitude ?
Related pic, for the lolz (it is simulation because I could not find it in a real environment)
Emergency/standby compass of an A320
http://www.flightsimlabs.com/index.p...eries-a320-3/#