Any reason not to paint window RO before flashing?

Hi –
I’m converting a screen porch to a sunroom by replacing the screens with new windows. Have it all framed & sheeting on; tyvec housewrap on the major exposed faces, will use flextape and such to actually flash the windows before installing them.
But I am backed up waiting on windows to arrive, so have some time on my hands. I also have a half-dozen old unfinished cans of paint in my basement I need to empty to dispose of….so in the spirit of two birds with one stone…any reason not to paint the bare wood with this as an added layer to help seal it? Seems it would provide some layer of insurance in the odd case that water gets in eventually.
Only concern would be that it might affect how the flashing tap adheres? i.e. if it were to peel or otherwise come undone the tape would come up with it. But seems most of it would soak into the wood pretty well. Or is there some obvious reason that I’m not thinking of (likely)?
Thanks in advance,
Jim