Google’s John Mueller was asked if sites that are verified with Google Search Console get crawled more often or at a higher priority. The answer is no, “crawling is independent of Search Console,” John said.

Here are those tweets:

Yes, you can use the URL Inspection tool to manually push URLs to be crawled faster but that is on a URL by URL basis and must be done mostly manually. Otherwise, just having a Search Console account won’t lead to expedited crawling.

Forum discussion at Twitter.