It's a fun idea but there's ample public reporting about how Google reacted to the rise of ChatGPT. There is reporting that Google was taken by surprise. You can be skeptical of that, but that's what the reporting says. ChatGPT went viral in Nov/Dec 2022, and by February or March Google was scrambling to stand up Bard as a viable competitor.
https://web.archive.org/web/20221221100606/https://www.nytim...
https://web.archive.org/web/20230512133437/https://www.theve...