Well, that's obviously not going to happen, but I wouldn't find it unbelievable if we saw that some of its components were imprinted with the names of real aerospace contractors or the like. The Space Shuttle's robot arm had its builder's logo on it, and I've seen photos of things like satellites or ISS components that had their makers' logos on them -- just as most vehicles and equipment down here on Earth are branded with their makers' logos. If anything, seeing all these futuristic spaceships in TV and movies without any manufacturers' logos of any kind on them is rather unrealistic.
That'd be cool, the warp engines are really Rolls Royce Merlin MK XV's, the phasers are Kalashnikov AK-670 PHASED Energy Rectification turrets, the shuttles are MiGs or Messerschmidts. That'd be very interesting.