Welcome to the ATK community!
Yes, you can compute the conductivity (or rather, conductance) of a nanotube. That is, the ballistic, coherent tunneling conductance, in the Landauer sense.
Mobility is however a "higer-level" statistical concept that also involves inelastic scattering processes, non-coherent transport, mean-free paths, etc. This is not included in ATK, and typically are treated with different approaches than full-scale atomistic (first-principles or otherwise) methods.
