No, makes a mess. Some people use tweak or other contact enhancer, but really, replace the connector like ForceFlow says. It's just worn out.

We use dielectric grease at my job for connectors that are exposed to road salt and other chemical hazards, as well as temperature extremes, and it's a higher current than the ribbon cables are.

I did mess around with using it on stubborn bulb sockets. While it did 'work' - it was REALLY messy when you went to change a bulb. Never again.

FWIW, the people that weren't used to it at work when they pulled the module out, they weren't too happy about the greasiness on their fingers, either.... so I asked them why they were holding the module at that point. It was literally a 1/2" portion of about 1 foot wide, and not in the middle either.

It would if it didn't get scraped away when you push the connector on (as designed). Of course, if you have a connector that's already not gas tight like the OP's ribbon connector, it might not scrape away enough, and it will still not make a good connection.

The old rule of thumb is never expect a chemical to correct a physical issue. Now that I think about it, the other contact enhancers are probably the same thing, just a more watery one. It's not like they are conductive.