If you have a version of the nano for a vehicle that uses CAN for the engine management ECU (2006 or later?) then maybe. If your EM ECU uses the K bus then I'm pretty sure they won't have 'activated' the CAN version of the engine management interface. What it definitely won't do is tell you what (non LR) manufacturer specific codes mean. This could be very confusing as some codes mean one thing on one car and something entirely different on another car.
If you just want OBDII on any car then a Chinese clone bluetooth ELM327 and the Torque App on a Android phone is pretty impressive for the money i.e. about £10. It does a pretty good job of listing the manufacturer options for the codes it knows about e.g. it does know P1590 on a Range Rover,although the description is a bit vague.