Was Gu Hang using the war to expand the alliance's influence?
Objectively speaking, yes;
Subjectively, he did indeed have this idea.
However, he felt no guilt about it.
On this matter, he believed he was doing the 'right thing'.
Given the dire situation in the Cosmos Domain, and even the Yunluo Sector itself being hard to defend, the Seven Horse Territory could not count on external reinforcements for at least a short term.
If the situation in the Star Domain deteriorated to a certain extent, the threat posed by the Iron-Tooth Clan would undoubtedly be greatly elevated by the Central Empire. By then, it might not just be the forces from the Eastern Cosmos Domain that would arrive, but the Central Empire might directly organize an expeditionary force to quell the disaster in the Dragonhawk Star Domain.
However, that would require a long wait.