Can seasonal allergies in children if not treated or maintained, cause asthma later in life?

No. If you have the genes to get asthma, it doesn't matter if you treat seasonal allergies or not. It will emerge whenever & wherever you hit the trigger events that let it come out. Many kids have seasonal allergies. Those that ignore them do not get asthma because they chose to live with them without throwing meds or shots at them.
Seasonal allergies. Allergies can affect various target organs, the nose as well as the lungs.So yes he can develop asthma later on in life.