Air gun sport and drug doping, would it be fair?

It all depends on what venue you're shooting in. If it's at an Olympic level or sanctioned by an international association/federation or such & it follows IOC (Olympic) rules MOST medications are prohibited even aspirin and alcohol. When I competed in archery in FITA, we had an archer that had to take prescription medication. The medication she took was prohibited but didn't worry about unless she won (which never happened).
Remember that in the last Olympics a Russian Gymnist was disqualified because she tested positive for cold medicine, she had the sniffles and took something for it that was prescribed by the Russian team doctor. 
They tend to only test the winners. 
 
It would depend on the specific medication, if prescribed by a doctor, and what its intended usage is.

I have hypertension and am on blood pressure medication to combat that. I am on a calcium channel blocker. It has gotten my blood pressure down to normal levels for a person my age. I will be 65 in September and my BP is now in the 120/80 range. I also go to the gym 2 to 3 times a week and am on a diet to keep my weight down. I can assure you that sitting behind the scope when I shoot FT, I can definitely SEE my EKG rhythm when I address my target. It does not diminish and I am constantly practicing to improve that and also because I just like to shoot.

Back when I was actively competing in events that meant something, namely the international pistol events with the intent of earning a berth on the US Shooting team and eventually qualifying for the US Olympic team, there were strict RULES about what was called blood doping. I could not use a BETA blocker for my blood pressure. At each major qualifying match and the US national championships, I would have to submit a piss sample under clinical conditions as soon as I finished shooting. If I was found to have any banned substances in my urine, I could have been banned from competing for a full year. That never happened to me. It did to others.

I tried my best to shoot the best possible scores by following the rules. I came close, but could not compete against the military teams that practiced all the time while I had to work a full time civilian job and practice when I could.

I shoot field target now. I practice, I know my guns, and I try to do the best that I can. I win frequently because I practice, but not all the time. Other than bragging rights, or personal satisfaction, why would anyone put some performance enhancing, or metabolic altering substance in their body, that could adversely affect their health to win a trinket? There is no money in what we do. We do it because we like to do it. It is fun. It is enjoyable. To try to win just for the sake of winning is fine, but to alter your bodily functions (heart rate, breathing, metabolism, etc) is wrong. If you do that, you are participating in this sport of airgunning for the wrong reasons. Think about what you are doing to your body. I have one friend that was into bodybuilding when he was younger. He was taking steroids. He is dearly paying the price for that now and doesn't have much more time on this earth.

A word of advise; don't do it. Practice as much as you feel necessary, shoot the matches because they are fun, and enjoy yourself and your friends and being a part of the airgunning community. It will mean more when you do win, and still give you a sense of accomplishment when you don't.

Hope this helps.
Best regards,
Mark