This depends on the chirality of the CNT. However, it is my recollection that yes, the propagation only occurs along one direction. However, the wave numbers that are allowed are more than one and are discrete. Unfortunately, I don't have complete notes on the derivation although I went over it about 6 months ago.
If you can find a 3D picture of the band structure, I believe that you will see that the the metallic CNT only has the conduction and valence bands meeting at one point (well, I think it's four points actually but I think it only counts as one point when using the Brillouin vectors. So this single point accounts for the single direction of the k vector and the periodicity of the Brillioun (How do you spell this guy's name fer crying out loud?) lattice is the cause of the discrete wave numbers that are possible I believe.
But if you are just interested in calculating the current that is dependent upon the situation. The CNT's are capable of ballistic transport, under these conditions the CNT's have zero resistance but there is a contact resistance due to the fact that there are only two conducting bands from the pi-bands. This results in a contact resistance of 12.9 kiloohms. This is only useful under specific conditions. In addition, I believe Burke has developed a transmission line model for the current if you are interested in an AC excitation. That's Peter J. Burke of UC-Irvine.