I can't speak to whether your method of adding an account will work or not, but I suspect it will. I always add accounts for the Mail App using the "Manage Accounts" feature within the App itself. I can say that accounts that are added via the "Manage Accounts" feature in the Mail App do end up showing up in the list of accounts in the system Accounts, Email & App accounts pane. Typically the first one that appears under the "Email, Calendar, and Contacts" section is the account you have associated with your Microsoft account, which shows up with an Outlook icon even if the e-mail account itself is not an Outlook.com account. In my case it's a Gmail account. Directly beneath that are accounts I added in the Windows 10 Mail App, which is why I presume your technique will work, too.
You do choose Google for any Google related service, in this case Gmail and it will also set up synchronization of contacts into the People App and the Google Calendar for that account into the Calendar App.
It is not possible to answer your question regarding receipt of all previous mail without knowing whether the client was using POP or IMAP access in whatever e-mail client they were using previously. If they were using IMAP they absolutely will get anything and everything they had access to before since all messages, contacts, etc., are stored on the e-mail server until or unless they are deleted. If they were using POP most POP configurations delete messages from the server either immediately upon download to the local e-mail client or some fixed number of hours or days after the initial download. When that occurs these messages are no longer available for future download into another e-mail client if one switches the e-mail client you're using.
These days I tell anyone setting up e-mail for anyone to use IMAP as the access method. The only real drawback, and it's very seldom an issue, is with access to very old messages if you are currently offline when you want to look at them, as message bodies are not kept perpetually locally when IMAP is used (at least not by default). Many clients allow you to set IMAP access such that all messages up to a certain age will have their message bodies retained by the client, but it's not often used since the vast majority of us have an internet connection virtually all the time. IMAP also has the distinct advantage of automatic synchronization of e-mail across multiple devices accessing the same account, where POP does not. It's a grand PITA to have two e-mail clients running POP, one on a desktop that's always on and another on a mobile device, where the desktop client may download e-mail and then those messages are removed from the server before the mobile client ever has a chance to see them. I once had a client with 4 devices who someone had configured POP on all of them, and it was a three-ring circus trying to figure out why certain e-mail was showing up on one device and not the others (or it was for her - I recognized the issue immediately because I've "been there, seen that" far too many times).
~ William James