Yes, wood will float. If you can wedge it in the mold so that it is held by friction that should be ok, but you have to be careful not to distort the sides of the mold too much.
Another option is to use some plastic mesh (something like 1/4" squares, or mesh bags from oranges or other produce) and cut a piece the size of the mold. you can fill the mold, then use large rubber bands to hold the mesh in place along the top of the mold. The mesh will be cut off and disposed of when you demold. You can also pour your resin through the mesh into the mold if that's easier. The mesh can also hold your wood down if it's stiff enough.
I'm not 100% sure about using mold release. Silicone molds demold pretty easily, but I think I have heard that some Stoner Urethane mold release can extend the life of silicone molds.