No. Super Smash Bros. Brawl (Wii) does not include a dedicated "Team Attack" mode where the game enforces teams and friendly‑fire settings.
Dedicated, matchmaking‑ready team modes (2v2, 3v3 with shared stock and friendly‑fire toggles) were introduced in Super Smash Bros. for Nintendo 3DS/Wii U and expanded in Super Smash Bros. Ultimate.