No. A dedicated Monkees Wii game will not be released.
Limited Run Games / Strictly Limited could print a "Monkees Collection" cartridge for Analogue Pocket or Evercade (retro handhelds) — but they'd need IP holder (Rhino/Warner) approval. Unlikely but not impossible for 60th anniversary (2026).
Verdict: 0% chance on Wii. Play their songs in modern rhythm games instead.