At least some of the datasets in
http://dataverse.ucla.edu are already on DataCite Search, which also used to be crawled by Google Dataset Search. So even if Google Dataset Search couldn't index records from a Dataverse repository, if the repository registered DOIs, Google Dataset Search used to get those records from DataCite Search. I haven't seen any news about this changing. Does anyone in the community know? If not, maybe we could contact the DataCite team to find out more.
I think it's be better that each repository takes steps to be crawled by Google Dataset Search. But it might be worth figuring out if anything changed about how DataCite Search exposes dataset metadata to Google Dataset Search. Maybe DataCite made a change for repositories that don't want their records appearing in Google Dataset Search.