Can I use Wally or Evosoda to search my deck for a card that is not in the current tournament format? For example, could I use it on Raichu to search for a Raichu BREAK after it rotates out?
Yes, you can. Even though a card may not be in the tournament format it still exists and can be searched for even though it is known to fail.
Source: TPCi Rules Team (2018-07-26)

Relevant cards

Note: All applicable cards may not be listed below.
XY1_116
XY6_107
XY6_94