Easy enough with some modifications. Make floats cylindrical. That would allow constant aperture at the bottom of container. Replace valve with a mechanical iris that opens and closes almost instantly as necessary. The friction in the iris can be reduced arbitrarily, making it work without losses. The control could be electronic. Again, power consumption can be made arbitrarily low.
So the construction is absolutely possible. That's not the problem.
The problem is that the float only floats when surrounded by liquid from all directions. What happens to the float that's passing into the container through the iris? Well, it experiences full pressure of the fluid from above and none from below. The net force will be down. It's very easy to show that no matter how many floats are in the fluid above it, the downward force on the bottom float will always be greater. (To fit more floats, you need a higher water column, resulting in higher pressure on bottom float.)
The conservation of energy actually becomes immediately apparent if you try to figure out how much work you need to do against the float to push it into the fluid through the bottom valve/iris. The amount of energy needed to take the float from outside and put it at the bottom of container is exactly the same regardless of whether you force the float into liquid from above or from bellow. The difference of potential energies in two situations is exactly the same, and so the energy requirement is the same regardless of path.
Long story short, the machine can't work, which really shouldn't be a surprise.