Have you noticed getting sick less since jaw surgery?

I'm awaiting a surgery date for double jaw surgery, and am a heavy mouth breather. I often wake up with headaches (assuming it's from lower oxygen levels during night due to mouth-only breathing?) and dry/sore throats.

The headaches and dry/sore throats often lead to sickness or just not feeling great in general, and was curious -- has anyone noticed getting sick less since getting jaw surgery, assuming it has expanded your nasal airways and allowed for better nose breathing and oxygen intake?