Does Apple Mail bring in 'old' (i.e., already existing) mail from webmail accounts?

I'm planning to try using Apple Mail for the first time.

It's not clear from anything I've read so far whether Mail can retrieve and store the user's already existing email (i.e., the emails that are already in their outside email accounts accounts before they start using Mail) or only the new incoming mail in those accounts, starting from the time the user installs and begins using Mail.

By 'webmail accounts' I'm referring to Yahoo!, Outlook.com, etc.

Can Mail download the full content of those accounts, and if so can that existing content be filtered to exclude email the user doesn't want in Mail won't be included in the download? 

Thanks.