Can it be that a few major cavities and tooth decay cause exhaustion..?

It can....: It can if you are experiencing a dental abscess or infection. Remember our dental health is uniquely intertwined with our general health. An infection your mouth will affect your entire body. I would advise getting dental care as soon as possible.

Possibly: If your body is fighting an infection due to tooth decay, it may be enough to make you tired. You should consult a dentist to get your teeth restored.

Infection: Cavities can cause infection which affects your entire system-see a good dentist as soon as you can.