Yes, but the ship is already being accelerated upwards by the surface of the earth at 9.8 m/s^2. If you were to lift it, you'd do it very, very slowly, so you'd increase the acceleration (temporarily) to, say, 9.8000001 m/s^2. The extra force required to do that is very small.
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.
Because this is physics I wanted to clarify that the ship is not being accelerated upwards by the surface of the earth at 9.8 m/s^2 it is being effected by a static force that is countering an opposing force that would cause it to accelerate downwards at 9.8 m/s^2 that causes it to remain in a state of rest. To lift the ship off the ground you not only need to out pace the difference between the static force in agreement and the opposing force - but the static force will not contribute to motion so you do correctly need a force that would result in an acceleration of 9.800001 m/s^2 in the absence of gravity.
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.
