No, it is not acceptable to do post-hoc tests on individual factors if the ANOVA says the factor is not significant. The reason is that doing so invites precisely the problem that ANOVA was designed to solve: that given many individual tests, the aggregate chance for a false positive increases greatly.
Actually, though, I don't think an ANOVA is the best analysis vehicle for the setup you describe. The reason is that drug_dose is actually a continuous, not a categorical variable. By treating it as a categorical variable, you are making it harder for your analysis to detect its effect: your test would have to see a clear step between two levels, rather than a trend of small changes between each level, because it does not know that the categories represent increasing levels.
I think a multilinear regression would be a better analysis vehicle. It will have no problem with your pretreatment variable, because a binary category can be safely encoded as a 0 or 1 value.