What happens when?

usually not enough output to use.
Unless it is a "high output" Moving Coil type. Then you probably can get away with it.
No other real problems.
Just most MC have far less output voltage than a Moving Magnet type.
If you try it and it sounds loud enough, then you got no problems.

You'll need to turn the volume on your preamp all the way up, and then go sit right in front of your speakers wearing a hearing aid . . . . . . .

Most MM inputs provide a 47K ohm load. MC cartridges usually need far lower load impedances, in the 100 - 2000 ohm range. In additin to insufficient gain you'll get response anaolies due to load mismatch.

Having said that, many high output MC cartridges are designed to work with a standard 47K MM input and will not have a problem with gain or impedance match.

That's too funny .......:))