Let's assume that a ship is traveling on the ocean and it sinks, what is the effect on sea level? Even if the effect is small, would it go up, down or remain the same?
It would go down.
In order to float, an object must displace a volume of fluid that weighs the same as the boat. In the case of a ship, this volume is less than the gross volume of the boat, including the air inside it. That's why it floats with the gunwales comfortably above the water. So when the boat is floating, it displaces some volume V, so relative sea-level goes up (second panel, below).
However, when the ship is submerged and full of seawater, it displaces a smaller volume than it originally did. If it didn't, it wouldn't have sunk (assuming it hasn't changed in weight).
Since it displaces a smaller volume after sinking, relative sea-level must go down. But it will still be higher than it was before the ship was launched.
The sea level should decrease. Consider a boat before it sinks. It must displace a weight of water equal to the weight of the boat to have neutral buoyancy. The material comprising a boat is more dense than water, thus is less voluminous than the displaced ocean. This displaced ocean volume will be realized as a rise in ocean height. However, once the boat sinks this volume of water is no longer displaced and this will be realized as a sea level fall.
Note that the sea level should be higher with a sunken ship than with no ship at all, so this answer depends on a working boat on the ocean surface being replaced with a sunken boat. Also note that the magnitude of sea level rise and falls being distributed across enormous surface area is likely too minuscule to be able to measure (e.g. smaller than instrument error).