I have a second email account that I had never added to my phone... I added it to test this for you.
In your sync settings for each email address, you can specify how many days worth of inbound mail should be downloaded and saved to your phone. The retention (3, 7 days, month, anytime) setting will determine how much mail is stored in your inbox. Mail stored in folders is not automatically synced, although you can tell it to do so when you view the contents of the folder.
Sent items seem to be the exception ... sent items are retained for the same time as the inbox (3, 7, etc.), but will not retrieve/sync email that was sent prior to the account setup on the phone. I set up the 2nd account with, call me crazy, anytime as the sync setting. I now have hundreds of messages in that inbox on my phone. Subfolders are there, but empty except for a command to sync this folder. I sent several messages from my 2nd account to the primary MS ID account and all the sent email was added to the sent folder, but no sent item history prior to setup.
I know this isn't what you want to hear. But given that I've had some email addresses for years and years, a sync anytime command would certainly crash my phone... so it seems they decided to protect users from their own potential brain farts.