A rub with a high salt content and heavy application will draw more moisture to the surface over a longer period of time, and this will result in a pasty rub...a marinade of sorts, if you will. No real harm in doing this with larger cuts of meats, but small cuts, especially if lean, may suffer enough moisture loss to the surface to become drier after smoking to finished temps.
As Pineywoods mentioned, a second application of the dry rub for a double dose and you'll be set to go.
Never thought about any possibility of bitterness as BarbeQueen mentioned...guess it could happen depending on the ingredients...possibly a reaction with the salt from the rub and moisture from the meat...don't know. I generally rub within 30-60 minutes of hitting the smoker, and often hit with a second dose immediately prior to smoking. I have done a few overnight or longer, depending on time constraints if I had quite a bit of meat to prep...putting smokes on hold due to weather is never an issue for me anymore...I'm sheltered well from Mother Nature.
Smoke on, Alex!