I would have to make a guess, honestly. Well - let's call it a "hypothesis"

For me, I'd have to test experimentally before I was really satisfied. Chemistry isn't my strong-suit, physics is.
Technically, I believe we have a mixture of liquid nicotine [miscible] and liquid PG [miscible] (and liquid flavors, be they oil-based or aqueous solution). In a mixture, the components maintain their distinct properties.
I found on PubChem the molecular weight of Nicotine as 162.26, the molecular weight of PG as 76.09 [g/mol].
My hypothesis is that you could concentrate the mixture by allowing them to separate given the weight difference. The flavor would also then be concentrated.
Another variable that strikes me is that PG is hygroscopic. So in the air, depending upon the humidity, I'd expect the mass to rise as it attracted water from the air.
Turning our attention to arenas I feel more comfortable in: By definition, evaporation happens only upon the surface of a liquid. By further definition, density effects evaporation - those more dense evaporating more slowly (again the reason for looking up the molecular weights). The kinetic energy of a molecule is proportional to its temperature, so increasing the temperature would increase the rate of evaporation. (that's why hotter cartomizers, or more wattage, increases the amount of vapor it produces, incidentally...). Rate of evaporation is also proportional to surface area.
Given those criteria, I would guess that since the nicotine is more dense than the PG, the PG would evaporate off faster.
I will say that PG evaporates VERY slowly, having very low kinetic energy. You could accelerate the process by placing the mixture in a shallow pan with a lot of exposed surface area, and by gently heating it.
I know there are chemists out there laughing at me right now. The _fact_ is: "
I don't know". That's one of those that I'd test via experimentation rather than calculating because my chemistry-fu isn't that great. But my physics-fu suggests that the kinetic energy would be greater for the PG, and it would evaporate off first. Whether you'd lose some concentration of the nicotine solution to evaporation in that time is a question-mark - especially if you sealed the mixture, allowed it to settle (increased vapor pressure to saturation), and then conducted your evaporation.
So, although invoked, I don't think I've really helped you along much!