The hyphae will grow into the log, but recognize that a large diameter log is a bigger food source for the fungi,so it will take longer to run out of food.
Mushrooms are produced at the end stage of the lifecycle of the mycelium. When it starts running out of food, it gets a signal to send out fruiting bodies. That is why you see a stump or a dead snag covered all over with mushrooms, all at the same time.
One reason that plug spawn works as well as it does is that it is a high concentration of mycelium and when you drill a log and put in the plug spawn, it takes off and quickly infects the entire log. Since the whole log is quickly inoculated, you get a nice flush of mushrooms when spawn is close to done eating. If your goal is to get regular production out of it, I would suggest randomizing the size of your pieces. The smaller pieces
should flush with mushrooms first, then bigger ones, and finally the whole stump.