No it isn't. Enterprise was used for ALT (Approach and Landing Tests) in 1980's, pre-first launch. Technically, it has 'flown', but not as part of a launch vehicle or into space. It was 'drop tested'.
Flight software testing only requires the computers and related avionics; currently, some of that is in Bldg 9 at JSC (I think - it's been years since I was there). Flight software testing is done in a variety of ways, including running it in the astronaut training simulators on emulated and actual flight hardware. One of the early flights, STS 2 or 3 IIRC, was delayed a coupla days cuz a bug in flight software. It had occurred in the simulator as well, but nowhere else. Flight crews didn't yet trust the realism of the GNC configuration in the simulator, so the simulator was considered the cause of the bug.
The SMS became a part of the testing process for flight software after that.
Again, this is personal comment only, does not reflect, and I am not authorized to speak for my employer or NASA.