Depends. It depends on the cyst: regardless, if you've had a persistent cyst for more than 3 months it neeeds to be evaluated.
No periods. The answer to your question is that "yes" it is technically possible for you to get pregnant, but it is very, very unlikely. In order to count on getting pregnant, you need a regular cycle that is triggered by increases in hormone levels, leads to ovulation, and is followed by a period, if you do not become pregant, to reset the sytem. Hormonal treatment can induce a period in your situation.