No, there isn't a mechanism within the Deserializer that can stagger the initial power-up current demand, but there are methods to produce a lower inrush current.
First you need to figure out the initial (inrush) and average (operating) currents. Then figure out what exactly is causing the high inrush current (is it caused by a capacitor, etc...)
If it is due to a capacitor, a smaller capacitor can be used to lower the inrush current.
Also, sometimes the cameras have switching power supplies, these cameras can be programmed for "slow start" which can reduce the inrush current. Large capacitors on the power input to the camera can be placed on the power switcher output to produce a lower inrush.