I don't personally believe that the difference in what they eat is enough to have an affect on the medication they take in. The standard concentration of amprolium is 0.0125% in most medicated starters, which is 0.125 g per kg of feed. The LD50 for amprolium in lab mice (ie the dose required to kill 50% of test animals) is 6.17 g/kg of body weight according to the MSDS. Concentrations for treating broilers go as high as 0.025%. Unfortunately there isn't much literature on quail out there, but I would be thinking that a quail would have to eat way more medicated feed than is physically possible before it started having any issues with toxicity.
Medicated vs. non-medicated, which is better etc. is an ongoing debate that everyone has their own thoughts on - some people swear by it, some people won't touch it.
I know every once in a while, back when I was hatching craptons of quail, I would get a batch that was just poor-doers. Never did find out why. 99% of the time I would lose one here and there but that's it. Then one day i would lose 75% of them for no reason that i could see at all. Then the batches for the next year would all be fine.