They were screwed long before capitalising on this was a real possibility. The damage was done to Kodak before the vast majority of consumers had fast enough broadband to share more than a couple of photographs a day.
Kodak was an obviously cheesy, out-of-touch, cheap-looking digital brand by 2000, and it showed (at least to anyone outside the USA). The Fuji, Olympus, Nikon and Canon compacts were better-designed, full stop, and Kodak really even had nothing good in the "office camera", "lab camera" or "art department camera" offerings (which Nikon owned with the Coolpix 900 series, and Canon with the G1/G2/G3).
People simply would not have bought into the idea that anything Kodak did was cool or fun. It was the same bad cheesy smiling family branding nonsense.