Whilst a manufacturing plant probably uses fabricators (though some low tech places may still use older machinery), using a fabricator doesn't necessarily make it a manufacturing plant in the sense of High Guard.
External fabricators make more sense for a large objects (if only becuase of the slight price reduction).
For a normal Fabricator it takes 14,000 chamber litres capacity for each DTon for TL13 that comes to MCr700 per DTon. A fabricator capable of building a 200-ton Hull is going to cost you MCr140,000. Even if you save half the cost by using raw materials it is going to take a lot of ships to pay back that capital investment. You would need to produce over 4500 Far Traders to break even. That assumes no power cost, no labour cost and no interest payment on the capital and that every component is TL11 or lower.
I don't see any reason it couldn't be done technically, but I doubt it would be economically viable.
It would make a heck of a story arc though