"Is the tartan official?" and "Is the tartan registered?" are two different matters entirely. In order to be considered the official tartan of the US Army, then it would have to be duly accepted as such by the US Army.

This acceptance is not a requirement for registration by either the Scottish Tartans Authority nor the National Tartan Register. It would be considered, strictly speaking, a fashion tartan named for the US Army.

Most all of the US military tartans would fall into this "fashion" category, with no official position as far as the US military is concerned.

I actually thought I remembered a year or so ago that the US Army tartan had received official recognition by the Army, but I don't see anything about it in the STA notes and I can't find anything with a quick Google search, either, so I may be remembering wrong.