If I used Steelix's "Gigaton Shake" on my previous turn, would Channeler allow my Pokemon to attack this turn?
Yes, the effect of Gigaton Shake would be removed, and your Pokemon would be able to attack.
Source: Unified Minds FAQ (2019-07-19), TPCi Rules Team (2019-08-01)

Relevant cards

Note: All applicable cards may not be listed below.
SM11_104
SM11_104
SM11_190
SM11_190
SM11_232
SM11_232