Does buoyant force vanish if there is no liquid below an object?

The question is posed as a thought experiment. So arguing with any complications due to limits of technology doesn't help in answering it.

The answer is yes. When you evacuate the space between the object and the bottom of the water vessel, there is no buoyancy on the object (which goes upward). There is however a net resultant down force on the object due to the water pressure difference between the top and the bottom of the object, pushing it down.

What complicates the matter (adding a little more reality to the thought experiment) is that the water to the left and right of the object exerts a pressure near the bottom which will make water flow underneath it. This then creates the pressure difference that causes the object to move up. But that's not really hydrostatics anymore.

The practical problem is the requirement that the block and tank have to have "very smooth" faces. A normal block of wood does not meet this requirement, so it can't form a seal with the bottom of the tank. Water can still get under the block and push it upwards.

Try the experiment with a plunger. The wood and rubber float, but you will be able to get it to stick to the bottom of a tank of water. Once the bell is pressed to the bottom, the rubber keeps any more water from getting under it. The water pressure above the plunger presses the plunger into the bottom, making it stick.