Naaah--that is probably the last thing you have to worry about when yak fishing. For most of us who are flats fishers and who fish inshore waters that rarely are more than about 6 feet deep, you/we will probably never see a whale unless one gets stranded.
Having said that, I did see something humongous this past summer just inside the bar at Shell Point, Florida. It seemed way too big to be a shark or a smaller marine mammal. It was startled by a passing outboard and seemed to run partially aground on the edge of the bar where it had to then work its way back into deeper water. Never did see it blow however, and even though I am a marine biologist and have worked all over the world, I am still not certain what this thing was. Possibly a very large nurse shark.
However, I often encounter pods of bottle-nosed dolphins. In fact, I have worked my Hobie Sport right into the middle of pods of about 6 individuals who were busting bait all around me on about three different occasions. I fold the Mirage drive flippers up against the hull and pull my paddle so as not to bump or hit them. Even though they were coming clear out of the water, they always managed to avoid me and dive under the yak at the last minute with no contact. Here are a couple of pics from about six feet away that I took at Sebastian Inlet last year on the Atlantic.
And that vid about a whale landing on some unsuspecting yakker was a complete phony, as Matt Miller indicated. It was put together for a Korean TV commercial. But it sure looks impressive, and has been on the Internet for several years now!