If you read above - Dropbox does exactly that...
> https://www.dropbox.com/help/space/file-storage-limit
They claim a limit of around 300,000 files - this user apparently has 700,000 files.
The Google sync client doesn't have a hard limit per se, but yes, the performance does similarly decline after a certain point - it depends on a number of factors, but it's possibly at 700,000 that you would see issues. It should be able to comfortably handle 300,000 though.
In fact, most Desktop sync clients experience similar things.
I do know this is something we're aware of and are actively improving. In fact, we have a new Backup and Sync client that we announced recently and should be going GA shortly.
There's no details I have to contact this specific customer to see if I can intercede, but if anybody knows, please comment here.
(Disclaimer: I work for Google, but any comments above are my own).