I do not know, but I think it is an intriguing and interesting idea. Growth of CNTs usually occur atom by atom, so I am not sure what would be the effect of radiation on such bond formation, particularly because radiation is usually "too strong" (keV's to 100's keV), and bonds are relatively weak (~ few eV's). On the other hand, gamma radiation is probably not what you might want, since it is weakly interacting. Alpha radiation might be what you want, but again, it might introduce too much damage. Maybe using SRIM/TRIM will help you visualize the interaction of alpha particles with mater. By the way, to my mind comes the image of how CNTs grow (I think like plants, for example, Revealing the Role of Catalysts in Carbon Nanotubes and Nanofibers by Scanning Transmission X-ray Microscopy Jing Gao1, Jun Zhong1, Lili Bai1, Jinyin Liu1, Guanqi Zhao1, Xuhui Sun), what would radiation could do in such process? Maybe create some radicals that can initiate the process, damage the bonds as they form introducing defects? Intriguing, but uncertain. Good luck.
Thanks for showing interest in my query. I am intrigued indeed, the radioactive ( unstable) interaction is going to produce some effects which are not provided by any other stable elements. CNT growth mechanism based on crystallization will be affected by the instability. Investigation is in process. And SRIM/TRIM is a good suggestion. Appreciate it. Would welcome more suggestions.