Yes, represent the Joker as an int with all binary 1's, like 7, 15 or 31. Represent the cherry and others with an int with only singe binary 1 like 1,2,4,8 smaller than the Joker. Leave zero unused. Then, using bitwise AND your condition is equivalent to:
(box1.BoxRank & box2.BoxRank & box3.BoxRank) > 0
Note that 3 Jokers will satisfy the condition too.