Once a document has been published (Version 1), has been crawled, and is available to search in SharePoint Online, if the document is republished with the next version (Version 2), does the crawl have to take place for the new version to be in search results, or will search return Version 1 until the next crawl is completed?
In your scenario, Search will return the last published version that the user has access to from the index. Version 1 will be returned until Version 2 in indexed. SPO uses continuous crawling and queries for document updates from sites. The update should be available in under 10 minutes.