You would have to apply but be prepared to be disqualified as asthma is a bad thing to have aboard ship. Shipboard fires (a common occurrence) fill compartments with smoke which can be deadly for asthma sufferers long before it affects a normal set of lungs. As an intel officer you would serve aboard ships for sure---the Navy does not make medical accommodations among intel officers. Had you completed an officer source program like the Academy or ROTC before you got the diagnosis, you may have a chance as the government has already poured a ton of money into you but that is very rare as the condition is usually picked up before you enter those programs too. Good luck but it doesn't look good.