PS: From some further experimentation, the account checking sequence does appear to follow the sequence in which accounts are listed in Account Settings; however, it is also affected by the server response time, as it appears to check one account at a time on each server.
In my setup, I have four accounts (#1-#4) on one server, and one account (#5) on another server. The accounts were added, and are listed, in the sequence #1, #2, #3, #4, #5. However, when I check the mail, Outlook always prompts for the account passwords in the sequence #1, #5, #2, #3, #4. It looks like Outlook processes the accounts in the added/listed sequence, but because both servers have a similar fast response time, Outlook prompts for the first account on the first server (#1), then while waiting for that, it prompts for the first account on the second server (#5), then after those two passwords are entered, it proceeds similarly through the rest of the accounts (#2, #3, #4), which are all on the first server.