My son's father is not involved and isn't documented in any way as the father. What obstacles would I face if I join the military & my husband isn't my sons father?

At this point do you have a custody order, do you have child support order.

Not involved and not having a legal stand are two different things.

He can of course come back at any time and ask for custody, and so on.

Also their step parent would have no real legal custody of them in case you were away for extended amounts of time