Why not? If they poll the same question (e.g. political party) repeatedly (e.g. in many elections) eventually you could build some kind of model of which parties poll-answerers are more likely to skew towards, or how much they shift compared to non-answerers. Not fundamentally a different process from other ways of removing bias from polls.
I believe this is not true, because at least ESS (European Social Survey) corrects for non-response, although how exactly is beyond my understanding of survey analysis. Each country reports the response rate as well. See [^1] section 3. Although ESS is much larger survey than simple opinion poll, there are political affiliation questions too (`^prtv.*$` variables).
[^1]: https://www.europeansocialsurvey.org/sites/default/files/202...
Sometimes this works out alright. But sometimes not. Too many factors in the universe to model. Never enough power to look at all them even if you knew what they all were. It works well when a few dominant factors are present but when its a million latent factors with technically every pairwise interacting relationship present in some degree, good luck.
Professional polls are either accurate or have a good reason afterwards why they weren’t.