Is it possible to have a period without ovulating?

A period is defined as the withdrawal bleed after ovulation. So the answer to your question is no. But remember, blood coming out of your vagina does not equal a period. Women with PCOS don't ovulate sometimes for many months and then bleed erratically due to overabundance of endometrial tissue. That doesn't mean they ovulated. Sometimes the birth control pill can thin your uterine lining so much you have break through bleeding on the pill. That is NOT a period either even though patients will say “I’m having 2 periods a month on this pill". Not correct use of the word period.