Can I study TKD with a back injury that may prevent kicking?

[JazzKicker]

You could, but it would be a bad idea.

Kicking can be really bad for your low back, especially if you overdo it.

I overtrained in my late 20's-early 30's when I did a lot of Tang Soo Do. Hundreds of kicks a couple of times a week, plus jumping and spinning. Not knowing better, I blamed it on a long commute and uncomfortable car seat. But really, it was overuse and biomechanics

A few years later I trained in Hapkido, and I learned to lower my head and relax (for things like spin & high kicks), not stay in such an upright position. It took the strain off my sacrum!

Another breakthrough was learning a Tai Chi form. This taught me a more relaxed, less rigid stance, and lower center of gravity. This would be good for your back no matter what else you do with martial arts.