Apple Mail: what happens if I Archive everything currently in my inbox?

I use Apple Mail for all of my various email accounts (1 Exchange, 1 Office 365, 1 Outlook, 2 Gmails), and my inbox is currently a big mess.

In the interest of time and starting fresh, can I just select all of the emails currently in my inbox (across all of my accounts) and Archive them to some giant folder?

If I logged directly into my Gmail, for example, what happens to the emails I archived in Apple Mail?

Basically I want to create sorting rules to stop this from happening in the future, but I don’t have the time to sort through all of my current messages at the moment - and looking at the big message number is driving me nuts.