Nope, you will still get carbonation, but it depends how much the bottles are leaking. I recently bought bottle caps for old kombucha bottles I have, their original caps were thrown away so I ordered what I thought were good ones. I filled almost 30 of them up and found out they were also leaking like yours, but they still carbonated really well.
If anything, it prevented the overly excess fizz that would turn my bottles into a nuke, my kitchen is much cleaner now.
I had the same happen to me with a few of my bottles. I would say that based on how much carbonation the bottles are leaking, it might not be a lost cause! I have had a few bottles that did leak too much, and the final kombucha was not carbonated at all and even had a bit of an odd taste to it, but that might not be relevant. On the other hand, I had a few bottles that leaked as well, but, they still carbonated pretty well, some even very well.
Test it out! See what happens with them, a slight leak is not the most ideal maybe, but it can still carbonate, so don't give it up!
