Naval races were more than Britain and Germany

Could Britain, the United States, and Japan keep racing if other navies were not part of the treaty system?

Yes; a treaty could not work cleanly if other major and secondary naval powers remained free to build around it.

The Washington settlement responded to a multi-power naval race that extended far beyond Britain and Germany. Britain, the United States, Japan, France, Italy, Russia, and South American powers all affected what others believed they had to build. Alliances and loopholes could also undermine limits if only some fleets were constrained.