Did Robb plan to incorporate the Golden Tooth into his new realm?

Unlikely. Robb’s offer of peace describes his kingdom as incorporating:

“…all the Stark lands north of the Neck, and in addition the lands watered by the River Trident and its vassal streams, bounded by the Golden Tooth to the west and the Mountains of the Moon in the east.“

If Robb had seized the Golden Tooth in battle, it might have been a different story, but it doesn’t seem like he was making any claim on that particular castle.