No. There is no evidence to support the idea that nicotine damages teenage brains. There have been decades of research into nicotine and smoking. If nicotine caused brain damage, this would have been clinically established by now - and not just in animal studies, but in real world situations. 

To isolate nicotine as the cause of any brain damage, you would have to demonstrate that nicotine use - and not any other contributing factor like sociodemographic status, family background, other drug use and so on - had been the sole cause. This could not be shown for smoking, let alone vaping.