It seems that there is more work associated with your option.
If A = all emails, P = number of pending and A>>P, then
his method: click "unread" P times
yours: click "archive" A-P times
A-P >> P
His method is less work.
his method: click "unread" P times
yours: click "archive" A-P times
A-P >> P
His method is less work.
In triage method A (his method), you first page through all your unread mail (1 click/keystroke to open the first, then A - 1 clicks/keystrokes to advance to the next conversation without returning to the inbox, and 1 final click/keystroke to go back to the inbox.) Then, once you've seen them, you select the mail you want (P clicks requiring dexterity, or A+P keystrokes; it's a compromise) and mark them as read (1 keystroke.) M_a = O(A + P) = O(A). (Because, as you said, A >> P.)
In triage method B (the "naive" method), you page through all your unread mail, and at each step, you either advance to the next conversation, or archive the current conversation and advance to the next conversation. (1 click/keystroke either way.) M_b = O(A).