Is gear retraction critical to a successful 'getaway' ?
Generally speaking, yes, but in some aircraft retracting the landing gear increases drag. Gear doors open, and the motion of the landing gear increases, rather than decreases drag.
In transport category aircraft, the takeoff is divided into "segments," each of which prescribe minimum climb gradients. The "second segment" climb is often discussed, being one of the most critical, and begins with landing gear retraction, and continues to until 400' minimum.
The first climb segment begins 35' above the runway and lasts until the gear is retracted. The minimum climb gradient during this time only stipulates that a positive rate of climb be achieved in 2 engine aircraft, or .5% in 4 engine aircraft.
This is really the critical point in the takeoff; getting away from the ground and to an altitude where it's safe to begin cleaning up in order to climb.