I think the series would need to undergo too much plot deformation to make Garibaldi going to Z'ha'dum realistic...in other words there isn't really any way to know how events would have unfolded because they would have had to have undergone drastic changes to get us to this point to begin with.
Anna wouldn't take Garibaldi to Z'ha'dum, which means Anna wasn't the one who the Shadows controlled. The obvious candidate is Lise, but that would necessitate changing events both before and after Z'ha'dum, since if Lise is Shadow-controlled then S4 needs to be significantly changed.
In the meantime, if Sheridan doesn't go to Z'ha'dum then I suspect the Shadows end up destroying B5, much as they were prepared to do before the Z'ha'BOOM. There's no reason for them -not- to destroy such an obvious threat to their plans, and no realistic way Sheridan's forces at the time could have fended off an all-out attack on B5.
A What-If we might have better ability to work with would be "What if Susan had been in Garibaldi's place?" The Shadows and consequently Psi-Corps would have abducted her instead...Garibaldi needing to hold things together on B5 would have been some interesting character development. Does the Edgars thing pan out with Garibaldi, or is that plot shifted so that an altered Ivanova ends up involved in it, minus the personal attachment? If Sheridan still gets abducted later on and Ivanova's gone, does Garibaldi take command of the fleet beating back Clark's forces? He never really struck me as the type for that, but Sheridan had reservations about Delenn, for instance, leading that fleet, and for good reason. I suppose Marcus and Ivanova could essentially reverse roles...Ivanova realizing that she loved Marcus after he'd been critically injured might be a bit of a stretch of her character though.