No you may not destroy their ship. Not even by taking their capital, nothing short of total destruction will stop their ship. BUT, there are ways to effectively stop them from finishing their project:
During the 100 years war, the english employed a strategy that involved not taking the enemy lands but instead, they would render them useless. Remember all that precious time you spent working up your precious lands with those workers?
PILLAGE-PILLAGE-PILLAGE and then bomb their land-improvements to bits, then PILLAGE-PILLAGE-PILLAGE and bomb some more. Don't waste time on taking their cities, just make them look like crap instead! Good units for this type of thing: Anything that flies. Move fighter about on carriers, taking out their vital resources (alu. has been mentioned) out, then their hammer-producing squares go, and then food\commerce in any desired order. A regular land army may also swamp areas on your own continent or go in with transports on continents. Being dominant in a military sense will probably let you do this in a MAJOR way.
