There's a real practical reason for that. In both of those wave pools there are a bunch of people. It's not like you're out in the ocean where people are spread out or people are on the beach. They are all over those wave pools and you can't really surf when there's that many people around.
So, no they do not allow boogie boards or surf boards in the wave pools at either Typhoon Lagoon or Blizzard Beach.
That being said, at Typhoon Lagoon they do offer surf lessons in the morning, and that's surf lessons you bring your own equipment. So you could bring your boogie board.
They also have a thing they do in the evenings, select evenings, where you can go and you can rent the wave pool for up to four hours. It's actually 100 waves. They'll send out a 100 waves. You can choose the height, but they'll send out a 100 waves, and you get to surf for a 100 waves. And it's for up to 25 of your closest friends. And again, you bring your own equipment to that.
So while you can't do it during regular hours, you can do it after hours.