If you parallel connect two or more different flashes then the sync voltage will eventually rise to that of the highest voltage flash. The sync voltage is usually derived from the flashes main high voltage source via a high value resistor charging a small capacitor. When the flash is fired this capacitor is discharged into a trigger transformer to produce a trigger voltage to the tube.
If multiple flashes are paralled together then these trigger charges are not independent any more and the same charge will be applied simultaneously to all of the trigger transformers. It is more than likely that all the flashes will fire o.k. but there is a possibility that one transformer could have a significantly lower primary resistance than the others and take more than its fair share of the charge causing the other(s) to misfire.
Again, I don't think any damage would occur.