If I use Phione's "Whirlpool Suction" Ability and target my opponent's Pokemon with Stealthy Hood attached I know the Pokemon with Stealthy Hood does not move. But would I be able to discard all cards attached to Phione and put it on the bottom of my deck?
No. Since Stealthy Hood blocks the move effect of Whirlpool Suction, the "if you do" clause fails and Phione stays in play.
Source: TPCi Rules Team (2020-02-13)

Relevant cards

Note: All applicable cards may not be listed below.
SM12_57
SM12_57