Yes it is possible, but will be difficult, just for the fact that your ovulation isn't regular. I have done some research because I have some medical issues and I wanted to see how they would effect me.
This that really suck out..
Abnormal periods means abnormal ovulation, you might want to pick up an ovulation meter, it lets you know when you are ovulating they can be found near the at home prego tests.
If you are overweight it is thought to lessen your chance of becoming prego
Last but not least, it takes most couples a year to conceive. If it takes longer than that you will want to check fertility levels with you and your partner.
But, you can become prego if you don't get your period as long as you ovulate. Grab the meter, its the first step to helping ya out.
(and I feel for ya on the periods, it'd be nice if they came on time wouldn't it?)