Another person I spoke to said:
Glycerin (Glycerol) has a density of 1.26 g/mL, so it is a bit denser than water. Since it is a polar molecule (the OH group), it should, in theory, be able to dissolve polar and ionic solutes, just like water. “Salt” being an ionic solute, should dissolve to some extent in glycerin
I guess the only way to find out if salt will dissolve in glycerol is to try it?