This is an interesting question.
How it works..............
A crystal is designed to operate at a certain frequency, into a certain specified load. Most crystal are specified to work into a certain amount of capacitive load, say 32 pF. In the case of a crystal-controlled FM transmitter, part of the capacitive load is in the form of a varactor, which is nothing more than a reverse-biased diode, with known capacitance vs voltage parameters. Audio is applied to the varactor, its capacitance changes, and you have FM!
Where it gets interesting (and probably too far out in the weeds) is how much the crystal can be "pulled", which in this case determines the frequency deviation. (Think of frequency deviation to be the equivalent of modulation level, in good ol' AM. IOW, how loud it will be.) The ratio of the crystal's internal motional capacitance to its holder capacitance determines how far it can be pulled.
Which is just a fancy way of saying really good hi-Q crystals are not likely to work in an FM transmitter.