Sea turtles can survive in the wild with only three flippers as many sporadic sightings of turtles with such injuries show - they learn to adapt to a missing limb just like humans. If they are missing a front flipper, they learn to compensate by using their opposite back flipper when swimming, for example. We currently do not know if a missing limb is going to significantly influence the general life span of these turtles, as systematic studies are not easy to conduct.
One or two missing hindlimbs is going to have a great impact on female turtles, as they use these flippers to dig their nests. Unsuccessful digging can lead to abandoned nesting attempts.
References:
Spotila JR & Tomillo PS (eds.) 2015. The Leatherback Turtle: Biology and Conservation. Johns Hopkins Press, Maryland, US.