Sorry, but that is soooo wrong.
This is all about impedance matching, and load - nothing to do with neodymium magnets. ECC mentioned it back a page or two. You have to consider a few things - the input impedance of the device you are connecting to, and the impedance of the coil. You can design a microphone with incredibly thin wire, so that it is more efficient and converting physical movement into electricity, or you can use much less delicate, thicker wire that can stand being inside a kick drum. The thicker and heavier coil and it's former will have more of a resistance to starting to move, and once moving to slow down at the other end of travel. The impact is mainly changes to frequency response, but also a different 'sound'. The lower impedance of one version compared to the higher resistance of the other also works against you by the mic trying to work the other way around - as in the connection to the preamp loads the coil, which actually dampens it. Typical preamps might well have an impedance of between say 150 Ohms up to maybe 1K or a bit more. In this range, the unwanted loading with some impedance capsules presents a good transfer and minimal 'back pressure' using descriptive, not science words. You can connect an SM57, with the transformer missing to a guitar amp - probably the worst combination, but if the amp has enough gain, it sort of works. It gets wrecked a bit by the capacitance of the cable, and the length, but apart from sounding a bit woolly, it works, sort of. You can take a loudspeaker output from an amp rated as perhaps 8 Ohms, and with care stuff it into a guitar amp expecting maybe a 50K pickup? It works. As an example of mismatches, I currently have the output of a Sennheiser IEM receiver, connected to the line input of a powered PA speaker. The mismatch means I have great quality, but the IEM is turned up nearly full and the volume on the speaker is high too. Turning it off makes a huge loud bang. The battery went flat, and I swapped it for a Trantec IEM 4000 - the output impedance of this is very clearly different. I need to have the volume knob way, way down. If I plug earphones into both of them - the volume is the same. The earpieces are 15 Ohm, the input impedance of the speaker is highish - not sure exactly, but probably 25K maybe?
This is what happens when you have impedance mismatches. If the mismatch works well, it may well turn a rather bright mic mellow, or just reduce it's output, or loads of other consequences. My advice is simple. try it and see. You cannot have a rule, because the transformer in a mic is there for a purpose - perhaps just to make it work on a wider range of kit without changing sound? You could design a mic that did not need a transformer, just by altering the windings - more/less winds and more/less thickness to the cable. Just don't allocate the 'better' sound to the mic mod - consider the mic AND your preamp, you have made it a combination. Your good mic could sound rubbish on a different preamp - something that does not happen very much with designed products.