If you are talking about putting the glue inside the holes in the core where the screws go... Nothing will happen, except for that you won't be able to adjust the tension without first having to break the bond. It will still move fine.
Unless of course you were to use a lot of glue, in which case putting in the screws might cause it to spill out and get inside the other parts of your cube. In that case, how much lubrication is still inside the cube might decide if it will move again or not.
If you have a problem with your screws coming out, it is better not to glue them to the core. The usual way to fix that problem is to apply a tiny bit of super glue to the end of the screw, let it dry and then assemble it. The added material will prevent the screw from coming out again. Or you could just use a product made for locking in screws: loctite.
The next time you make a post, it might be wiser not to write in all capitalized letters. It's annoying to read.