Not losing its reputation as a whole, but losing the reputation of being the leader in this field? Sure.
When they released BERT there was no doubt that they were the leaders. Even laymen heard about it.
What AI advances do laymen most talk about now? DALL-E, Stable Diffusion and ChatGPT. AlphaCode and LaMDA gave some headlines but not even close. Everyone is too busy trying ChatGPT to pay attention to those.
Google publishes plenty of other ml based papers.
Assuming in any way that Google might loose it's reputation because of imagine is very very far fetched.