No, the track packs are standalone games, and you can play them without owning any of the other Rock Band games.
Rock Band Track Pack Volume 1 is a standalone gameplay companion to Rock Band, the collaborative, competitive, and single player music game.
(On the linked page, you can see a similar blurb on each of the packs)
Do note that on the Wii, you won't be able to export tracks from a track pack into any of the other Rock Band games. (The Green Day version is the exception. You can export that to RB3 on Wii) This means that if you later buy Rock Band, Rock Band 2, or Rock Band 3 for Wii, you'll have to put the Track Pack disc back in the console to play the songs that came with it.
You can view the full export table on the Rock Band website.