its very possible. i thought i was never going to get pregnant due to my irregular period but I'm 38 weeks today and i couldn't be happier.
Irregular cycle may mean you do not always ovulate. This can happen due to PCOS or other reason. Talk to your ob: a simple blood test can check whether you ovulate and they can make your cycles more regular if necessary.
its possible as long as your ovulating...which can be very hard to pinpoint ovulation with irregular periods. i had very irregular periods for a while so I told my dr. and they ran some blood tests to make sure my hormone levels were normal, which they were. They can also tell whether or not you ovulate. Im just over weight which can cause your periods to be irratic! But with my first son I started birth control for a couple months to try and regulate my period, came off and within the first month I ovulated on time and became prego (not to say this would work for u but it did for me lol ). You can also track your basal body temps and use ovulation predictor kits. Also learn the signs of ovulation such as egg white discharge or slight pain in your right ovary. Dont stress too much about it because that can make you not get preg! I know your struggle so I wish you all the luck in the world, it can be very discouraging :-/