If you want to eat a banana before you singing go for it.
Things you eat or drink don't touch your vocal folds, so they aren't going to coat or otherwise mess with them.
My recommendations are drink plenty of water, avoid alcohol, and practice.
Another thing to avoid is extensive speaking. Normal speaking is surprisingly detrimental to ones singing voice.
Other folk remedies for voice include flat, room temperature Coca-Cola. I don't think anyone has demonstrated efficacy of any of these techniques, but another big factor in effective singing is mental state. If a placebo ritual helps get you in the correct frame of mind to sing, then it might just be worth doing. The destructive alternative is to get intoxicated before a performance.
While eating a banana should most certainly not result in a banana-grease coat on your vocal cords, it will be all over your throat. Might just be a little bit like hand lotion for it.
My recommendations are drink plenty of water, avoid alcohol, and practice.