I just realized – right in the very beginning (think "The Rising"), they wouldn't have been able to hold Atlantis if not for Sheppard's inclusion in the expedition.

If they'd traveled to Atlantis without Sheppard, one of two things would have been the inevitable outcome:

a) Due to the lack of genuine ATA gene carriers, Atlantis wouldn't have turned on so many systems when the expedition first set foot on her decks. They would have used up less power from the already almost depleted ZPM and would have had sufficient time to evacuate all personnel to another planet (perhaps Athos). They would have left the city to sink under the ocean, would have been cut off from Earth until/unless the Daedalus came looking for them in several months' time, and would perhaps have perished with insufficient supplies/been culled by the Wraith on Athos.

b) Despite the lack of genuine ATA gene carriers and the subsequent lower initial power consumption upon the expedition's arrival, Atlantis' ZPM's power wouldn't have been sufficient to allow for a (complete) evacuation via the city's Stargate. Dr. Weir would have most likely felt the need to stay behind until all other personnel had left. Either the whole expedition or those of its members not among the first to leave would have perished in the ocean water flooding in. McKay would have drowned, and Dr. Weir and the rest of her staff wouldn't have been able to escape via puddlejumper because they wouldn't have had a pilot with the ATA gene with them. The original timeline wouldn't have been altered to allow for the failsafe to be installed as shown in "Before I Sleep", and history would have repeated itself.

Which, in short, means the expedition would have been screwed without Major Sheppard. Although it seems very likely that the Wraith wouldn't have been woken prematurely, and so the Pegasus galaxy would have enjoyed a few more decades/centuries of (relative) safety from culling.

So that day in McMurdo - would have head or tails triggered a better outcome? A worse one? Hard to decide.