Yeah I actually found the reference - it was a Star Trek book I read when I was a kid (not canon and not sure which one) that referenced the fact that the Borg and the Dominion were fighting each other - and the Dominion was winning the war with the Borg until they lost those ships in the wormhole - then things started turning south for them.The Prophets/Wormhole Aliens prevented Dominion troops from transversing the wormhole. DS9: Sacrifices of Angels. The Dominions had only the forces they could muster from the Alpha Quadrant in their fight against the Federation/Klingon/Romulan alliance. Dukat believed the 2400 ships sent from the Gamma Quadrant would have been enough to defeat the Alpha/Beta Quandrant alliance.
Whether they were fighting the Borg or not isn't the reason they didn't send reinforcements from the Gamma Quadrant.
That said, had the Romulans not turned, the Alpha Quadrant probably would have been lost anyway, at least that's the story DS9 paints. Seems like a small # of ships tho, to take on the entire quadrant, lol.