A better indication would be a recording pulse oximeter that keeps track of your blood oxygen level during the night. If your blood oxygen level falls "below normal" (typically below 90-92, although there are reasons that a lower score would still be "normal"), then you almost certainly have some sort of sleep disorder, most commonly OSA.
Another indication of sleep apnea is nocturia (night time urination). As I understand it, the trigger that causes your heart to beat faster/harder during an apnea event is the same trigger as the indication of excess fluid in your blood stream that causes your kidneys to produce more urine. Hence, the frequent need to urinate during the night.
Mouth-guards are designed to adjust the jaw position so that the back of the tongue does not obstruct the airway as easily, thereby reducing OSA and reducing snoring. However, mouth-guards are only effective in treating mild-to-moderate OSA.
Now, wearing a nighttime mouth-guard certainly can't hurt. However, it might not be a complete solution, and CPAP might still be required. At that point, one must ask oneself just how much nighttime stuff they are willing to put up with. I don't think there are many people that use CPAP and wear a mouth-guard. I know I don't, but I invite others to chime in to disagree.