The dock draws some power, so yes:  you do need a higher capacity adapter to run both the dock and the system at full speed.  
Just bought DA 310 USB C hub and tried the hook up the dell power adapter (45 W) through the DA310 with my XPS 13 9370 but it showed slow charging. Is there a compatibility issue? Any ways to overcome it? Do I have to change to a higher wattage power adapter?
DA310/XPS 13 (9370) Compatibility - Power Delivery