Will you get a period if you didn't ovulate?

No, not quite.

Menstruation is a very specific function, you will only menstruate if you have ovulated. You can however see vaginal bleeding for other reasons, you can get bleeding that is very much like menstruation and unless you're monitoring your fertility you wouldn't know any different.

There is then of course withdrawal bleeding that you get on hormonal Birth Control, you don't ovulate with most forms of hormonal birth control but you get a menstrual-like bleed as a result of the drop in synthetic hormones when going from active to inactive pills.