I understand your question in a way that you would use polynomial modelling to derive features that you would use as input for your logistic regression.
This is absolutely fine and makes total sense. As long as your features are solid and sound from a domain perspective, this is a great approach. If you can model understood cause effects in your features, go for it!
I think in reality often „the best“ model is not even needed. The pipeline needs to be good enough to solve your business problem in an efficient way. Side note: Maybe „data quality“ can have a stronger leverage than the „model“, see also this thread on data-centric AI.
Best regards
Christian