Yes, snoring can have serious implications for one's health. First of all, snoring impairs the sleep quality of the one who is snoring. Second, it impairs the sleep quality of those who have to try to sleep near the one who is snoring. "Sleep apnea" is a serious condition associated with snoring. Or stated better, sleep apnea result in snoring. Increased blood pressure may be associated with sleep apnea or the health of one's heart may be affected by this condition.
Therefore, the answer is Yes, snoring may have serious implications for our health.