It's a bit of an apples and oranges situation here. Given that you're a fruit lover and are looking for a tasty treat, the actual flavour isn't as important as overall quality and satisfaction.
And to that end the D7000 certainly belongs in the fruit bowl alongside the D600. But at the end of the day the D7000 is a 16MP DX camera nearing the end of its life in Nikon's active product line whereas the D600 as you know is a 24MP full frame FX camera released only months ago.
They have lots of similarities and share some technologies principally auto-focus and the main control dial. But there are also significant differences and improvements in the D600, not the least of them being the larger FX sensor.
The salesman isn't far off saying you'll get every bit as good performance out of an FX lens on the D7000 vs the D600 but it's not the full story by any means. Sure for most use the average viewer couldn't tell the difference but in practice for the photographer the field of view is different, the depth of field different and the final images have more dynamic range and greater pixel density from the FX D600.
I could go on but the bottomline is that your inclination to buy a good FX lens and keep the D7000 for now sounds fine. Clearly you are FX-curious and when the D7000 has either given up the ghost or you're ready anyway to invest in an FX body you'll have a great FX lens to go with it.
Yes FX glass works fine on DX bodies (given the differences noted above) but DX glass on an FX body not so much.
In no way would you be 'wasting your money' on a D600 though. It is an awesome camera - but then it is twice the price of a D7000 so it better be!