I would argue that exposure time and exposure concentration is not a criterium for carcinogenicity. On the specific topic. There are many different types of CNTs, which exhibit significantly different properties. However, if your statement is that CNTs are carcinogenic and you ask if you can use carcinogenic compounds as drug delivery systems, then my answer would be: No. Drug delivery systems should be safe to use. However, some colleagues argue that CNTs are very interesting for drug delivery, see the link. One particular important aspect if you want to consider CNTs would be certainly the aspect ratio of the material you want to use and how homogenous you can obtain it.
Although carbon nanotubes may be carcinogenic, there are certain ways around this problem such as coating them with a non-carcinogenic material such as silica.
Liu, J., Wang, C., Wang, X., Wang, X., Cheng, L., Li, Y., & Liu, Z. (2014). Mesoporous Silica Coated Single-Walled Carbon Nanotubes as a Multifunctional Light-Responsive Platform for Cancer Combination Therapy. Advanced Functional Materials, n/a–n/a. doi:10.1002/adfm.201403079