I wake up with a mouth filled with disgusting yellow-whitish sputum that smells horrible. Is this a sign of pneumonia?

Possibly. Most of the time, pneumonia with a lot of mucus has cough along with it. People with underlying COPD or tuberculosis can cough up phlegm and long-term sinus problems can cause drainage in the mouth, especially in the morning. Acid reflux can also give someone mucus and very bad breath in the morning. This does not sound like just a severe "cold", so contact your doctor.