Assume: Your DRY senses are infallible. Repeated behavior in your code reeks to you; it’s nails upon the chalkboard.
Question: Does keeping DRY in the forefront of your mind guarantee that you will notice when you should be seeking a design pattern?
It seems from what introductions to design patterns I’ve seen has been working around supposedly “needing” to repeat code. Is this an OOP truth?
The possibly more easy question: Is there ever a time when dry will lead you away from OOP design patterns?
IMHO that depends on the specific pattern. If you have the GoF patterns in mind: lot’s of them are aimed at “separation of concerns”. By factoring out a specific concern like object creation (Factory pattern) or object cloning (Prototype pattern) you will bring that part of your code dealing with this concern to a central place, making the code more DRY.
Other GoF patterns like Flyweight or Proxy have a different nature, they are aimed at more efficiency or less complexity. Those patterns are mostly orthogonal to the DRY principle.