AACK!
That stuff will slick them up, alright, but axle grease is cheaper. Doesn't do any damage that I'm aware of, unless you count glopping up the string as "damage."
My friends and I tried all kinds of tricks in the old days before we gave up and changed strings more often. We used to pull the strings and boil them, used string slick stuff (silicone in a can) and finally gave up on the notion that we had to have some magic bullet to make it all work. There's no magic. Just keep the instrument clean, use decent and recently changed strings, and leave the magic bullet for someone else to bite.
If you're using medium strings on an acoustic and your fingers hurt, try three things. 1 - play more often; the fingertips may be soft; 2 - consider changing guage to something lighter, even if only on one or two strings; 3 - you may need to look at your fretting technique.
This is off the track, but it bears repeating - If you're hand is cramping up all the time, fingers getting tingly or numb, or you are getting back problems, STOP NOW and listen to your body!! Something is wrong and will get worse if you don't change it. Nobody wants to see a guitar player wearing a carpal tunnel brace. . . You can keep playing with this stuff going on if you figure out the body mechanics and learn your limits.