Servicing Interrupt while it disabled for some period
What I would suspect would happen is that when a particular event occurs, the interrupt flag is set. If all interrupts are disabled, then only the flag is set and no jump instruction is issued. When you enable interrupts, if an interrupt flag was set, then the corresponding jump instruction would happen. 

But you're best bet is to read the datasheet for the microcontroller because it will tell what would happen.