It would cost them nothing extra to do so - as demonstrated by the isolated Alpha Quadrant beachhead force, they can produce ships and soldiers like there was no tomorrow, so sending all they have towards Alpha and then spending two and a half weeks replenishing the Gamma stock would be the sensible thing to do.
Naturally, the "long shot" force would face some problems: none of the original Jem'Hadar would survive the journey, and the Vorta might get too many ideas if there weren't Founders aboard to command the force. And since such a fleet would only be launched after the events of "Sacrifice of Angels", the Link would already be infected and the onboard Founders would soon die.
Still, we have the scary scenario of a fleet consisting of nothing but fanatical eleventh-generation Jem'Hadar on a holy mission to wipe out all the Alpha cultures, without any Vorta or Founders in command and with all the White factory ships under direct Jem'Hadar control, arriving at the Federation's doorstep around 2440-50. Although if their weapons were more or less on par with Alpha ones in the 2370s, they would probably be badly outclassed at that later date.
Difficult to see Odo taking charge of anything, what with him having been party to the genocidal attempt at the Link's life. He'd be pumped for information, then for a confession, and then slowly tortured to death. Also, difficult to see the Dominion subjects even finding out that there had been a war, let alone this resulting in any sort of changes in the Dominion. If the Four remained on Alpha, and came there early enough that they weren't infected with the bioweapon, they would be likely to continue furthering the agenda they had during the war, regardless of whether they could make contact with the Link or not.
Really, we have no idea about the contents of the treaty signed in the finale - would the Founders in Alpha (if they even exist!) remain in contact with Gamma via the wormhole, which supposedly still allows ships and messages through?
Timo Saloniemi