Suppose you made a lightsaber shaped like a Y, and in a battle fought with the one going straight. If you activated the other blade when you and your foe crossed blades, it would go right through them before they could block it, right? Is this possible?
Yes. In fact, something very similar exists in Legends: called the crossguard lightsaber or forked lightsaber. The only one described was used by the Jedi Master Roblio Darté during (and shortly after) the Clone Wars:
However, I don't believe he ever used it in the way you describe.
Although Roblio's secondary saber blade was only knife-length, in principle there's no reason it couldn't be full-sized; we have evidence of both variable-length lightsabers, and double-bladed sabers with multiple activators.