So what if the Shroobs came a bit later than usual? Mario and Luigi are in Bowser's gut and Bowser himself is still snoozing in Cavi Cape, so they can't intervene. Just an all out battle between Fawful's army and the Shroob army at their strongest.
Who wins and why? How will the battle go? Remember that Midbus + Fawful/The two Princess Shroobs won't be on the frontline most likely.
Probably the Shroob Army. They have better technology, equipment and greater numbers in terms of infantry. Considering that most of Fawful's army is just the Koopa Troop where most of the enemies are rather incompetent, I'd say Shroob's army would probably be superior and win.