The shooting script would suggest that they did make it to Parliament:
PICARD : Riker, with these "peace" delegates and all, I do need some rest. Take charge, Number One.
The "cloud" in far b.g. as WE SEE the Enterprise go into WARP SPEED EFFECT.
Obviously they have some destination in mind...
And although we don't see them again in the TV show, in the DS9 Young Adult Novel "Arcade", we learn that the peace process did not go well:
Rotor shrugged. “The Anticans are the mortal enemy of Selay. Honor
must be defended at all costs.”
Honor was just another word for dignity and respect. Jake knew that
sometimes people had to fight back, as when the Borg attacked the
fleet on their way to capture Earth. But sometimes honor was better
served by turning away. The Selay and the Anticans had been denied
membership in the Federation because they could not settle their
differences. There was no honor in that.
Later still, we see an Antican serving aboard the USS Atlas in TNG: Lost Souls (set some 10 years after the end of the DS9), suggesting that they have attained Federation Membership, the usual pre-condition of which is peace with their neighbours.