This looks like a good option for us in May 2020. One of the things we want to do is take the boat to Greenwich and visit the museums. I can't seem to find if the London Card with Oyster is valid on hop on/hop off boats (or if hop on/hop off boats even exist!). Appreciate any insight.
You can use Oyster cards on the Thames Clippers but these are point to point fares. If you have a Travelcard loaded onto the Oyster you get a discount. If you are getting on and off frequently a River Roamer ticket might be cheaper although you will need a few on and offs to make it worthwhile.
I have only ever used the London Pass which does include a Thames River Boat Cruise.
For any option such as this, it is important that you price out your "must sees" and then compare with the cost of the pass/card. There will be some on this forum that will automatically say these are bad deals. However, that isn't always true. Only you can determine if a pass or card is right for you by working the numbers for what you want to see.
One interesting bit of cost saving is that 4 day version of the London Pass is usually available for a 3 day price through Costco travel.