Dead time in Synchronous Buck converter
There is no problem since during the dead-time the current will flow trough the body diode of the FET discharging the inductor, very similar as a non synchronous buck. After the dead-time the FET is turned on bypassing the conducting diode. With this action you can reduce the losses since the voltage across the FET will be much lower than the forward voltage of the diode. 

All in all, Synchronous Buck is all about reducing the forward losses on the Buck diode. There is no change on the operation states of the converter itself. It will work in CCM, BCM and DCM given that you have the right dead-time.