No. The displacement is all that matters here.
Related: Stand on a scale and pull up on your shoelaces. No matter how much force you pull with, you will be unable to lift yourself from the scale, or even to decrease the weight it displays.
Discussion
Good analogy (at least for the ping-pong ball).
But would there not be a downward buoyant force exhibited from the steel ball?
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There would not be.
Example:
Stand on a scale and put a cup of water at your feet.
Tie a string around a rock and hold it.
Note the weight.
Allow the rock to dip into the water.
The scale will remain unchanged.
Negative bouyancy only means than an object will sink if not suspended. It is not an added force that needs to be considered, especially considering that the steel ball is externally supported and negative bouyancy can not apply as a result.
Your example would reflect the ball being suspended from the bucket, not the ground.
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That's fair, but the result is the same either way. No additional forces to consider.
Since it is supported by the ground, all downward force is applied to the ground and not to its side of the system.