Not if the microphone is intact and the wiring is symmetrical!
Phantom power is 48 V DC voltage that is applied to BOTH signal conductors of the XLR plug (contacts 2 and 3) opposite the 0 V potential (contact 1, microphone housing).
For current to be able to flow, there would need to be an electrically conductive connection between the moving coil contacts (or the secondary winding of the transformer in ribbon microphones) and the microphone housing. As such a connection does not exist in dynamic microphones with correct wiring, current cannot flow and therefore nothing happens to the microphone. However, caution must be exercised in the case of older microphones, which sometimes have different plug connectors and different internal wiring. As correctly described in the operating instructions for most mixers, all microphones (or wireless receivers, DI boxes...) should be wired first and only then should the phantom power be switched on. Accordingly for removal, first turn off the phantom power and then unplug.