Yes and no. By combining standard AI with some extra triggers it should be possible. However with the standard AI alone it lacks the required intelligence.
I do believe they actually due use transports as I recall seeing goblin airship thingy in comp stomps. However this is easy since air can move pretty much unrestricted.
The problem is with water transports. The AI has no concept of water and ships. It might be able to hire ships and it might be able to build a ship yard if water is inside its base. However the AI is totally unaware of land to water interaction so will have no idea where to land.
The main problem is the AI will constantly try to find a route to the enemies by land, not possible, which will result in periodic performance problems and overall incompetent AI. You need to detect this happening and then shove it over to a trigger system to handle this case. When the units are on the target you can probably give them back to normal AI. However I am not sure how the AI picks targets so it might be that the actual target pick system itself breaks if it cannot path by land to the target base.
By using a trigger system that runs in parallel to the AI, one could possible handle these problems. The trigger is responsible for deciding where to move ships and when/where to load/unload. The naval management (making docks / getting ships etc) might also need some trigger help.
The irony is SC2 handles this perfectly yet has no concept of water. The AI will easily use transports to reach islands but you cannot make an accurate simulation of water.