First, it is important to clarify terms. Custody and placement are completely separate issues. Custody is the right to make decisions for the child. Placement, on the other hand, is what most people mean when they refer to "custody." Placement is the schedule of times each parent has the child.
Assuming you are referring to placement, the chance that this somewhat absentee father will get more than occasional placement is vanishingly small, but the decision will depend on innumerable factors. I suspect that the father will be awarded one or two weekends a month, with visits supervised until the child is comfortable with him.
I agree with the attorney above. Definitely contact an attorney soon to give him or her a chance to prepare.
Sign up to receive a 3-part series of useful information and advice about child custody law.