Yes, the "three foot" model was used to film some special effects scenes of the U. S. S. Enterprise in outer space.
The "three-foot" model (actually 33 inches long instead of 36 inches) was completed and delivered on December 14, 1964, and was used to film all the special effects shots of the Enterprise in space in "The Cage", the first pilot film, up to December 24, 1964.
The eleven foot model of the Enterprise was delivered on December 29, 1964, and was used to film one special effects scene in "The Cage".
The "three foot" model was used to film the opening title sequence used in all episodes and for additional scenes in some episodes. Episodes which included scenes of the "three foot" model include: "Where No Man Has Gone Before", "Tomorrow is Yesterday", "By Any Other Name", where it was used for special effects in space scenes, and "Requiem for Methuselah" where it appeared on a table top as the original question said.
I asked for information on this subject at the Trek BBS site:
This is supposed to be a list of all shots of the Enterprise, specifying which of the models were used: