The meaning of online learning is to learn one instance at a time. The online/offline labels usually refer to how training data is feed to a supervised regression or classification algorithm. Since genetic programming is a heuristic search that uses an evaluation function to evaluate the fitness of its solutions and not a training set with labels, those terms don't apply.
Once the fitness of your GA/GP's population approaches a certain threshold, you can apply that solution to your application, and continue to run the GP, switching to a new solution when a better one becomes available.