The webapp can send your data wherever once it has the data, chrome won't log http requests if they were made server to server etc
A native application can do that too.
Isn't it the case for any app?
The logic is a native app can make a direct IMAP connection to the mail server and you can check it is doing so where as a web app has to send the login details to a server which does IMAP for the client and you can not see this last part.