There would still have to be a fairly large number of non-native Thamnophis introduced into an area for it to affect the long-term gene pool of a population, assuming they don't have some amazing super gene that gets highly selected for.
Think about what you said one of the main consequences would be; reduced fitness. If one or even a couple hybrid litters of reduced fitness end up in the wild, assuming they are selected against or neutrally, then it would not take long for genetic drift to remove those genes from the population.