Assuming maximal interface fluency with GMail, you actually perform [on the order of] the same number of input actions for both. Remember, in order to take care of the messages, there has to be a point at which you initially read them. You can then combine the read + file steps into a single triage step.
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).
I also use the unread status for stuff I could go back and respond to, I then archive stuff older than 90 days in my inbox. Having 3 months of email I can search on my BlackBerry is handy when I'm away from a computer.
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).