Yes. At the moment, this is done using Aspire Snapshots, so both full crawls and incremental crawls will traverse the site or list depending on the root url, with the difference that during incremental crawls only adds, updates or deletes will be indexed.
For a discussion on crawling, see here.
SharePoint Online has a secret threshold that once reached by our connector will start throwing HTTP 429 errors. We have implemented the practices recommended here by Microsoft but it's still possible to reach the threshold.