Yes he did.
I read the research notes and I looked at all the sources.
There is no doubt your conclusion is correct.
Also, adding one more piece of evidence:
In Soldatregistret he has the patronym "Gustafsson" which is correct, since his father's name is Gustaf Henrik Blåfield.
https://www.soldatreg.se/sok-soldat/
Search: Soldatens namn: "BRUS Johan Jakob"
Centrala Soldatregistret
BRUS Johan Jakob
Släktnamn: Gustafsson
Född: 1772
Död: -
Antagen: 1793
Avsked: 1806
Aktnummer: VR-06-0105-1793
Regemente: Västmanlands regemente
Rote: Lilla Rocklunda
Kompani: STRÖMSHOLMS KOMPANI
Socken: ODENSVI
Torpnummer: VR-06-0105