The initial sync fetches the top 20 (or so) emails from Inbox, and zero for the other folders. So essentially it populates the emails from that point onward, and doesn't try to fetch old emails automatically, but does give the user the option to do so if desired. 

We have resisted implementing a feature to fetch past emails, with the belief that a Mobile Client should target optimum mobile experience, which is NOT to fetch the contents of the entire mailbox, rather to make the most recent information available, while giving the user an ability to manually fetch, or otherwise do a 'Server Search' to find anything specific from older emails. 

Google's own app guidelines highlight that Mobile apps should emulate a 'cache the most needed stuff' experience, as oppose to building a database of entire contents of a user account. 

If you need to review any emails older than the retention date, you can use the 'Search -> Server Search' option to view anyemails. 

That said, a feature is in progress to allow the users to fetch past 1-3 months worth of emails if they prefer.