Well, I suppose the only way to figure out which time of day is being used (it's obviously not *hour*, or everyone would be having identical games all over the place) is to start a bunch of games during the same minute, and see if you get the same items more or less. Obviously people will always be getting a ton of coeff 1 and 2 items, so paying attention to which coeff 3 and 4 items you get would be more helpful I'd imagine.
In terms of seconds, it would be harder to try and start more than one game in the same second (possible if you're quick on the tab switch.) I don't think it's when you finish loading the game, but when you actually click the flash area to START the game that the item lists are loaded (just a theory).
With that said, maybe you could start a game at say, 9:00 and 30 seconds, and then set your clock back a minute, and then start another game when the clock says the same time again? I don't know if that would work; you programmers tell me.
At any rate, you're right, if it's milliseconds, then forget it.
Also something to take into consideration: if you ever actually found a way to get the item lists in different games to be the same, it would only be the list; you wouldn't get the same items on the same levels, and how many items you picked up would be dependent upon how many levels you actually played before losing your last life. You might have had a golden mushroom in a game's list, but if you lose before level [insert number here] you wouldn't see it anyway.
Sorry for the novel of a post.