Full immunity is unlikely
Let's give an example of a drug used in copious amounts in current society. Alcohol!
With alcohol use you can see that people do get higher tolerances. They need more alcohol to get the negative effects. I went to a court once where the accused was found after an accident with a blood alcohol percentage well over what normally would be deadly. His survival was attributed to tolerance.
There are DNA differences as well, besides typical physical attributes. From a better way for the liver to break down the alcohol to simply having a larger size. All can influence the alcohol resistance.
But have you ever heard of someone never feeling the effects of alcohol?
The imperative word is resistance. At a certain moment the biology and tolerances reach a limit. You will get inebriated, you will eventually die from alcohol.
This isn't applicable to all drugs. Yet most will follow the alcohol example after a fashion. Even with some serious biological adaptations over generations it is unlikely to becimebecome immune. But the body might not feel the need for such adaptations. It is surviving. It is reproducing. It isn't being harmed, at least not on a short scale. The body could very well have a form of homeostasis that includes the drug.
So even with generations being drugged there is likely to be no tolerance response big enough to become for all intends and purposes immune.
And even if you find immunity, you can use a variant or different drug to start all over again.