Through Jump Gates yes - its just another ship.
 
Its more difficult with jump ships as the shipyards are quite large, so you need very big jump engines.

oh man, I need to.  I just got my first energy weapons scientist with a greater than 0% bonus (23 years in) and I captured enough  beam tech from the alien empires that I can now begin a complete overhaul of the armed forces.

By not blowing those shipyards, actually, I saved a lot of time and money-- some of them are pretty nice and the planet has plenty of population to slave in them.  The redesigns will occur over the next year, and the construction will begin full swing once they hit candidate status.

Well, as said in another thread, you can apparantly go on offensive tug runs which disables the shipyard (and I doubt the NPR can do much to get it back).

That's just part of the FUN.

With regard to damage, rather than get into slipways being reduced in size, with the complexity involved if it is trying to build a ship larger than the reduced size, I have stayed with a similar model to planetary bombardment where slipways are either destroyed or unharmed by a hit. However, given it will be a lot easier to hit shipyards now I have made it harder to destroy them.

Each time a shipyard is hit, there is a chance the hit will destroy a slipway. The percentage chance of destroying a slipway is equal to:
(Damage / Capacity ) * 10000

In other words, if a shipyard with slipways of 5000 ton capacity is hit by a missile with a ten point warhead then the chance of one slipway being destroyed is: (10 / 5000) x 10000  = 20%

If the last slipway of a shipyard is destroyed, then the shipyard itself is also destroyed.

Source

So you will in fact never be able to reduce the maximum tonnage of a shipyard by damaging it.