Autoimmune heck is where I generally hang out. I've had AS since I was about 13, diagnosed at 18, and am going strong at 40. Strict Paleo, in my experience, is the only way I can eat. I started with Carol Sinclair's book "The IBS Low-Starch Diet" (I don't have IBS, but she applies it equally to AS), moved to Prof Cordian's Paleo books, and now devour any info I can get - the best recently being Robb Wolf's book and podcast.
Can you heal while on meds? I believe you can, it just depends what you mean by "heal". I don't think the underlying damage that inflammation has wrought can be undone - there will always be a certain background level of pain that you or I may require medication to deal with (no shame in that). Paleo has the potential to heal your gut, which is the gateway for all kinds of inflammation and other nasty things. I've come on and off meds over the years and am now still taking Celebrex. Does that mean I'm not healing or that Paleo isn't working? Not in my experience. I slowly allowed starch and non-paleo foods (including a ton of beer this summer) back into my diet and the consequences were disastrous. Major frequent flares that kept me off work and doing the things I love. Not to mention gaining about 15 unwanted pounds, which is killer for people with arthritis. I've been very strict for about 6 weeks and have dropped the 15lbs, have tons of energy, and pain is manageable. I will never let those foods creep back in again - it really scared me straight.
Whether paleo ever puts my AS into remission is actually immaterial to me. It would obviously be wonderful, but the many other benefits that paleo brings (leanness, energy, metabolic regulation, cardiovascular health, wicked sleep, and lower systemic inflammation) are enough to convince me. It minimizes my pain and keeps flares at bay. I'm able to sail, work out with weights, play ice hockey, and ride my road bike. I believe my diet has everything to do with that.
I think the only way you'll ever know is to go as strict as you can for as long as you can - the recommended 30 days isn't long enough for people like you and I to see major changes in pain and inflammation. I'd be happy to share any experience I have or resources that have worked for me.
Best of luck,