Yes. I might say "My brother and I have had a lot of twists and turns in our relationship." This means that we have probably had a lot of surprises that affected our relationship with each other, or other unexpected developments such as betrayals or fights.
If I say "The movie's plot had a lot of twists and turns," it means that unexpected things kept happening that changed where the story was unfolding.
It does not mean literal twists and turns, but figuratively if you think of the story or the relationship as a string or a ribbon, it would not go in a straight line.