Can some individual-level predictors included in the regression model be excluded from the poststratification frame?

In multilevel regression and poststratification (MRP), do all individual-level predictors included in the regression model need to be available in the poststratification frame? For example, if the poststratification frame provides population information only on province, age, gender, and race, is it still appropriate to include additional individual-level predictors, such as education or income, in the logistic regression model? Any help is appreciated.