For reference, the 4th is normally in the vicinity of the Cappellan and Sarna March's, with a division or so usually sputtering around in St Ives
As it relates to us, this doesn't matter.
The 4th Army on Tukayyid fights against the Bears first, and then the Falcons as a reinforcement unit. Since I rolled out the Falcons as your OPFOR, we'll be focusing on that portion of their engagement on Tukayyid. The 4th is a largely green army, so having a merc unit experienced in the fighting the Clans in general and the Falcons in particular makes sense.
I'm doing a little bit of more in-depth research on Tukayyid, and have come to a couple of irritating conclusions. Primarily, no day-by-day timeline exists for the Battle of Tukayyid. Additionally, specific events seem to be mutually-contradictory, for example, it's pointed out in Lost Destiny in a conversation between Ulric and Focht that it took ComStar ~2 weeks to drive off the Bears to get reinforcements into the Falcon combat zone. However, reading the Falcon Guard novel, it's possible to count the rough number of days between the time the Falcons landed (100% certainty on May 1st), and when they fled the planet...that number is somewhere between 4 and 8, but certainly no more than 8 days. The Bears and Falcons landed both on May 1st (every Clan but Wolf did), and so the time simply doesn't and cannot synch up.
Here is a brief list of sources examined:
Jade Falcon and Wolf Sourcebooks
Tukayyid Scenario pack (has no dates at all!)
Comstar Sourcebook
Invading Clans Sourcebook
FM: Warden Clans
FM: Crusader Clans
Era Report 3052
Lost Destiny novel (has dates; only applicable to a small subset of Clan Wolf)
Falcon Guard novel
Sarna
Thusly, I will have to conclude that while we will be adhering to canon in "broad strokes", this game will be necessarily less canonically-accurate than, say the events on Sudeten. Apologies. I personally blame FASA.