Open source, as in corporate outsourcing software maintenance to free labour? No. Free software, as in four freedoms? Yes, because you could install your own firmware that doesn't show advertisements.
That's what the whole GPLv3 debacle was about after all.
Stallman may have not imagined this specific scenario, but he absolutely did conceive of owner-hostile software that could not be replaced.
Theoretically, yes, but in practice almost everybody would just run their Ubuntu Fridge in a stock configuration.
You could, but would most people? Most people voluntarily subject themselves to garbage adware-ridden SmartTVs even though this is a problem you can solve with a £12 dongle and no software installation at all. If the humble HDMI cable defeats the average person’s technical ability, what difference would it make if they could technically install their own firmware?