I think it pretty much goes without saying that any Tudor house in North America doesn't date to the actual Tudors. (-: 'Mock' just sounds a little too pointedly sniffy to me, as if the house were trying to be something it's not, a parody of a house, when in fact it's just one style among others.
More common collocations are probably mock trial, mock indignation and mock horror, mock turtle soup and mock turtleneck (now why those two? hmm ...).
The same is true for Gothic churches -- you could call them neo-Gothic, Gothic revival, etc., I suppose, but the risk of confusion with the original is surely vanishingly small, along with the number of rich Americans who import entire houses. (London Bridge, on the other hand ...)
I'm not sure that's universally true -- neoclassical is a fairly established term in architecture, for instance. But on the other hand, I don't think anyone would flinch if you just said classical, as long as the building wasn't in Greece anyway.
I've never heard of 'Jacobethan,' and it sounds particularly ugly as well as arrogant. I'd stay away from that one.