Well, keep in mind, I’m fairly sure Illyrio’s plan to get Dany to Pentos would have involved trying to get her together with Aegon and get her dragons under his control.
Dany and Aegon showing up as independent rival monarchs was not part of the plan up to mid-ADWD, and if it hadn’t been for Tyrion you likely would have had Aegon showing up at Meereen as one of Dany’s suitors, like Quentyn but with sex appeal (sorry, @poorquentyn, but it’s true) and one of the best armies in Westeros at the moment she’s under siege.
The problem is that Tyrion completely deconstructs Aegon’s Hero’s Journey, and so instead of the Hidden Prince Marrying the Princess and Training His Dragon, Aegon’s destiny is to become the Mummer’s Dragon who will take the Iron Throne to the cheers of the mob, only to be roasted alive when the Slayer of Lies comes to take what’s hers.

So the personnel shifts in Essos turn out to have been really crucial: sending Barristan means Dany doesn’t get assassinated on the docks of Qarth (which would have been a major setback, but would have cleared the way for Aegon ultimately), but because Jorah has his own plan which doesn’t involve Illyrio, Dany doesn’t go to Pentos, so that plan is scotched. The problem here is that Illyrio is trying to work at arm’s length (which is good tradecraft, but there are…well, tradeoffs) across two continents, and unlike in cyvasse or chess, the pawns have wills of their own:
“Which plan?” said Tristan Rivers. “The fat man’s plan? The one that changes every time the moon turns? First Viserys Targaryen was to join us with fifty thousand Dothraki screamers at his back. Then the Beggar King was dead, and it was to be the sister, a pliable young child queen who was on her way to Pentos with three new-hatched dragons. Instead the girl turns up on Slaver’s Bay and leaves a string of burning cities in her wake, and the fat man decides we should meet her by Volantis. Now that plan is in ruins as well.”
And so do the best laid plans of cheesemongers gang oft alay…