Sort of... Some anovulatory cycles do indeed have periods, albeit that they tend to be a bit different (lighter/shorter) than normal periods. Though if you have lighter/shorter periods, that is not necessarily a sign of anovulation. Example: My periods last 2-3 days and are abnormally light... but Im still having a very obvious ovulation each month around CD16.
Generally, if you do not ovulate, you do not get a period. Such is the case with women who are on birth control that stop ovulation (the shot) or are breastfeeding and have a lack of ovulation due to that, and thus no periods.
Also, if you do not get a period and you are not pregnant usually that means you did not ovulate/ovulated later HOWEVER it can also be a sign of something called a functioning cyst, where the luteal cyst does not rupture as it is supposed to. One of the ladies on here is dealing with that now. They tend to be nothing to worry about and clear themselves up, though in rare cases they grow too large and will need to be taken care of. While these are common, it is not all that common that they hold off AF.