Highly unlikely since Google has been playing around with their own chatGPT called LaMDA that they are now making into a product called Bard.

I think that Microsoft could have had a chance if they decided to do this before even introducing the world to chatGPT, everyone would have been talking about Bing, but now everyone knows chatGPT and everyone is gonna be talking about Google's Bard as an alternative to chatGPT and not as an alternative to Bing/chatGPT.