not really, chatGPT can crawling whole web more frequently; google searching engine update its' indexing/data via keep crawling down the whole web, not sure how frequently, maybe several times a day, so that, you can get almost live-data;
part of data inside chatGPT is also from web crawling, generally, re-learning the whole chatGPT model is very expensive, however, OpenAI might have other strategy to keep model learning new data by incremental manner, it is pausible thing; if that is feasible, chatGPT can also provide live-data as google do;