Other jet boats probably are as well but I do not have first had experience with them.
Every Yamaha boat that I have seen has a scupper drain at the stern. This drains water from the rear of the cockpit out through the scupper valve. This scupper system drains rain water or water that has splashed into the boat.
The scupper does not drain water from the bilge or engine compartment. That water is handled by the bilge pump. The bilge pump should always be on when the boat is in the water. The bilge pump will cycle every few minutes to check for water and pump out any that is found.
If you happen to take a wave over the bow or side of the boat it is important to keep going and either get on plane or keep the bow elevated. Doing so will decrease the likelihood of taking on additional water, will increase the rate of flow through the scupper and will concentrate bilge water near the pump.
Our boats handle water in the bilge or in the cockpit area very well. The engines will continue to run until water gets into the air intakes at the top of the engine. The cockpit will hold water that drains through the scupper without ever entering the bilge. Even if the cockpit and bilge fill with water the boat has sufficient flotation that it will not sink.
I have been in a poorly maintained Yamaha boat that the dealer was demonstrating when a clean out of plug blew, the bilge was filled with water and then more than half of the cockpit filled with water. The bow remained above water where
@Rana, the kids and the dealer remained dry. I was at the stern holding the cleanout plug that would not lock in place. My legs were wet but I was not in any danger.
If your boat takes on water at some point please do not panic. If you get on plane or can keep the bow up you will likely be able to drain the water out. You should drive towards shore in case of the unlikely scenario of needing to abandon the boat.
Even if you forget to install the drain plug at launch the same principles apply. If you can keep the bow up you may be able to reverse the flow of water into the hull while the bilge pump does it's work. Once you believe you have reduced the volume of water in the bilge jump stop the boat, jump into the water and install the drain plug. I have experienced this issue in fishing boats and have seen the water in the floor drain out while the bow is elevated.