Heck of course it would work. Back then I practically drowned my whole cube in an oil based lubricant and it turned out ok. A little over exaggeration, but you can kind of see what I mean.
I got two different lubricants I use. both from the same brand. "Basta"
they both say "PURE silicon". one is on a bottle and one on the spraycan!
the spray works (makes the cube smoother) magnificantly better! I can apply and it is all set in 5 mins. but with the bottle it takes at least over night to dry out!
With the grease, I just took out an edge and just injected it into the cube. Then I just worked the grease to all the parts of the cube. It works wonders. Give it a night to fully sink in.