There is definitely a connection, be it to a high kick or even a thigh/torso-height kick executed with torque. An over-tightness in the hamstrings and/or tight or poor conditioned lower back can cause problems. Often times issues with the hamstrings will be interconnected with the lower back in any event, and vice-versa.
I never put much thought (mainly focusing on leg and hip flexibility) into the place the lower back has with kicks but a while back I strained my lower back and hamstrings on the right side while powerlifting performing deadlifts. It wasn't a tear but quite a strain and my hamstring was quite tight and needed a lot of work. Once my hammie had healed up I noticed at karate training when throwing high kicks repetatively that my lower back would hurt afterwards, sometimes pretty badly - something I never experienced before. The issue has gone now through addtional rehab work on the lower back (and a lot of yoga actually) but it made me realise that issues with the lower back can play into how we perform our kicks.
An overly tight or damaged lower back comes into play when we chamber the knee high and when we torque through the hips.
As a throw-away, I would add I am trying to keep up as much yoga as I can alongside the stretching and conditioning I do. It's a time thing as always, but yoga seems to really benefit an MA's training and conditioning (particularly if you want to be in it for the long long haul). Outside of striking, from a grappling perspective it has improved by upper body and shoulder flexibility a lot.