If it didn't have an expansion/overflow tank then it would just puke it on the ground. Downside of not having one is when it pukes, the coolant you lose......you lose. If there is an overflow then the coolant will be returned to the radiator which in turn will keep the radiator full.
If you don't have an expansion tank, then adjusting the level in the radiator to keep the expansion within the radiator is what needs be done.