(I assume this is an equivalent problem to the lifting problem, as the extra pressure they'd be fighting would be that of the ship displacing water.)
I do believe this is probably one of the solutions that's being investigated but I also believe it's
1. Super expensive to construct an impromptu dam under water
2. Floating a listing ship can result in more severe listing if you're not careful (See, for instance, the fact that when a ship beaches itself while the tide is out it's initially bad news - and when the tide starts to come back in it becomes significantly worse news.
Learning and humor are fun together!
Let's assume it was possible. Would the force of lifting that much mass be enough to shift the earth in a measurable way? (I'm assuming it would be a lot stronger lifting it into the air than what floating on the water produces, but have no idea what the math would be)
Note that ships actually are accelerated up and down in the Panama canal, which has locks. (The Suez doesn't.) That amounts to pretty much the same thing. It doesn't matter whether the forces are transferred to the earth via a column of water or a column of air.
Since the static force in opposition won't contribute towards upward motion you actually need to supply the full amount of force to lift it - not just enough to barely nudge the need by .00001 m/s^2
In terms of whether that force would cause any effect the answer is yes (because everything is an effect) and effectively no since as ridiculously heavy as this container ship is it is absolute peanuts compared to the mass of the earth nuclear explosions that produce megatons of force are still immensely negligible, ditto for super massive volcanoes. A volcanic explosion large enough to derail the earth's rotation by a day would definitely be an extinction level event for all of the complex life forms on earth. But, that said, every little thing does contribute in its little way.
Lastly - yea, the presence of locks in the panama canal does mean that ships are regularly accelerated upwards and downwards without any noticeable effect - if that change in elevation was executed by explosives or chinooks there would be slight variations in the force but they'd be mostly inconsequential on the scale of things.
Actually it is:
https://www.thegreatcoursesdaily.com/einsteins-experimental-...