The difference in voltage you would see being wired from there versus straight from the battery is negligible, and will keep you from having a parasitic power draw when the bike is off. The meter you are using has two power + leads, one to power the meter (make the numbers light up), and one to actually go to the metering circuit to measure the voltage. Both use the common - lead for return path.
Newer meters use one + lead for both the metering circuit and the display, which is what I am using. But mine is a bit larger than the one it appears you will be putting in the foglight switch hole.
Personally I would not put it there, it prevents you (or future owner) from using that location in the future for a fog lights system should you decide to install one later. I put mine in the little black panel area over by the right pocket key lock. Installed electric grip control there also.
Edit: see you posted since I started typing, that you have LED fog lights already. So disregard that portion.