Per the Wikipedia link, online learning "learns 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 really apply.
If what you're asking is if the output of the GP algorithm (i.e. the best phenotype), can be used while it's still "searching" for better solutions, I see no reason why not, assuming it makes sense for your domain/application. Once the fitness of your GA/GP's population reaches 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.
One approach along this line is an algorithm called rtNEAT, which attempts to use a genetic algorithm to generate and update a neural network in real time.