I use LOTS of various sled pulls. Not only for the lower body but also for the upper body. I'm careful when talking about 'carryover'. Carryover means that the gains on one exercise (e.g. sled pull) directly leads to proportional gains on another one (e.g. squats).
If we take that definition then no, there is no carryover from sled to squat.
HOWEVER sled exercises WILL increase squatting (and deadlifting, power clean, power snatch, etc.) performance if used properly.
Here are some guidelines..
DO NOT limit yourself to only one movement pattern; the results will be limited. For the lower body alone we use 5-6 exercises, not counting prowler pushing (in other words 5-6 exercises that you can do with the sled). We used:
Backwards dragging with the knees bent 90 degrees (more quads, especially vastus medialis)
- Forward dragging (although we prefer to do pushing with the prowler) for overall involvement
- Forward dragging with the torso bent forward (more glutes and hams)
- Pull-throughs (glutes and hams)
- Backwards dragging with the leg only slightly bent (quads and calves)
Sideway dragging (whole hips musculature)
Sled dragging can help you increase your squat by increasing lower body muscle mass as well as recovery. But to make it work you must use proper workout nutrition around it.
We do it frequentely 3-4 time per week, and we do a lot of volume. For the lower body I find it to be more effective to focus on only a few strength lifts and a lot of sled volume. You will build more mass, recover faster and keep your nervous energy high.