The kind of material you're talking about is called "metal matrix composite", and such materials have been used for their mechanical properties for a long time. Some electrical brush materials are also MMCs.
The relative properties of carbon nanotubes and pure copper suggest that the addition of buckytubes would make the copper stiffer, harder, and less ductile in proportion to the quantity of fullerenes in the mix. It would not necessarily change the surface qualities of the copper or the techniques required to join to it. Keep in mind that all electrical joints to wires have different resistance than the wire itself.
My guess is that carbon nanotubes in copper would affect its workability more dramatically than they affect its conductivity. At some point, different motor architecture with larger radius bends, or with ribbon rather than round wire, might be required. These changes could offset some of the benefit of the wire's improved conductivity.
While you're thinking about what subtle rewards there might be in using nanotube-copper MMC wire rather than pure copper, keep in mind that carbon nanotubes are like super asbestos
to living tissues.