They can (at least in some cases), especially if covalent attachment occurs. See

https://www.researchgate.net/publication/221856988_Site_specific_interaction_of_the_polyphenol_EGCG_with_the_SEVI_amyloid_precursor_peptide_PAP(248-286)?ev=srch_pub

for an example (SDS PAGE with Nitroblue Tetrazolium detection of polyphenol). There are other examples in some of the references. Another example is

https://www.researchgate.net/publication/236275533_Toward_the_Molecular_Mechanism(s)_by_which_EGCG_Treatment_Remodels_Mature_Amyloid_Fibrils?ev=prf_pub

Article Site specific interaction of the polyphenol EGCG with the SE...

Article Toward the Molecular Mechanism(s) by Which EGCG Treatment Re...

Thanks much Jeffrey! But don't polyphenols normally tend to bind non-covalently (hydrophobic interactions, or H-bonds) to proteins?

Oh that's interesting, so you are saying there is a method with which you can stain/track polyphenols in an SDS-PAGE? Is this method feasible?

I should be more specific. The test is actually for quinones, which are the autooxidation products of EGCG. EGCG (and many other polyphenols) are readily autoxidized and can participate in a variey of adduct formations. The degree of autoxidation varies with the actual polyphenol.

As far as pure polyphenol staining, I don't know of any stain for SDS-PAGE.

Polyphenols have a very strong tendency to bind with the proteins both via hydrophobic and hydrophilic interactions.... this is the reason why still tannase activity is measured indirectly in terms of BSA released... The sample buffer would not help much in breaking the bond between the polyphenols and the proteins. If you wish to see the same whether your polyphenols are bound to your protein or not, you can put chilled acetone to your sample. This will selectively precipiate the protein. You can resolubilise the protein in buffer of your interest and then run an SDS-PAGE of control vs acetone precipitated protei. A difference in the molecular weight would confirm that polyphenols are associated with your protein sample

I have done work on soluble tannin-protein complexes and used mobility shift in SDS PAGE as an indicator of covalent complex formation. this only works well in a model system with a few proteins.