Unfortunately, AS is on the list of conditions that MAY disqualify you from military service. You should talk to your supervisor/recruiter about it. I believe you must disclose it, or you risk some serious trouble down the road.
As for the biologic, you may feel relief immediately. It's more typical, I think, for your symptoms to gradually improve over a period of weeks and to continue to improve for up to 6 months, at which point you'll hit your point of maximum relief, i.e., the relief you experience at 6 months is likely what you'll continue to experience for as long as the drug continues to work for you. If you have experienced no improvement in symptoms at the 3-month mark, the drug may not work for you at all.
I take Enbrel, rather than Humira, but they're similar. I'm in remission (my rheumy has told me this; I'm not just diagnosing myself), meaning I experience very few symptoms on a day-to-day basis. But I still have flares from time to time, and I cannot run or play golf (or tennis, which would be my preferred sport) because the trauma from those activities increases my pain levels and can trigger flares. I have found other things to do however, which have become as important to me as tennis used to be. Some people do continue to golf, etc. Look at Phil Mickelson, for example. He has psoriatic arthritis and has been on Enbrel for years.