It is absolutely possible.
You don't NEED Meds to recover from anxiety, but that is not to say that Meds and/or professional expertise cannot help in the recovery process.
The trouble with anxiety is - the path to recovery is a minefield - so sometimes Meds and professional help can speed up the recovery process and sometimes they can literally just get in the way.
I am afraid there is no one set formula to recover from anxiety, the symptoms may be common to us all and we may all have a flight or flight mechanism that activates in the same way, etc. - but the REASON for the mechanism being activated, the symptoms being displayed, are usually pretty unique to us all - and that is why recovery can be arduous.
Meds may treat the symptoms and help stabilise the mechanism, etc. but if you truly want to beat GAD then you must address the REASON
GAD and in my experience finding out the reason, uncovering the CAUSE (and not just treating the effects) is where the real task is at and that can be a short journey or a long one depending on many factors and the biggest one of those is luck.
This is the real trouble, the real pisser with anxiety - nobody, and I mean nobody, really knows what has made us "faulty" for sure (including us) and so we have to embark on a process of trial and error to see what makes us feels better and what makes us feel worse until we find a course that makes sense and we recognise as "the REAL problem here" and when we find that then we can work on that and really begin to get better.
Until that point we are stuck with trial and error I 'm afraid. Now like I said if we are lucky then we may stumble across the reason for our anxieties in a pretty short period of time and begin to get better quickly, however if we are not so lucky then we will have to spend more time searching for the underlying cause of our anxiety until we strike "gold".
So Meds (or therapy) may help with that as they may help you get back on a more even keel, so that you start to look at your GAD in a more intelligent way, from a more anxiety reduced perspective, etc., etc. and help you strike "Gold" quicker - OR alternatively Meds (or therapy) MAY simply cloud the picture and MAY put you on a few wild goose chases instead.
So which way should you play it? - I have no idea - but the reality really is that recovery is trial and error. So that means don't narrow your search and be prepared to explore ALL your options.
Now that doesn't mean you have to go out and get Meds tomorrow, but it does mean that Meds should not be dismissed as a viable option either. My best advice is - whichever way you choose to go next, trust your intuition, listen to your gut instinct as it REALLY DOES know whether what you are doing is working or whether it is not - it really does.
Hope that helped - a one line reply turned into a thesis