The Pocket Trumpet is a 'fun sized' member of the brass family but is it considered to be a 'real' instrument?
In terms of manufacturing it is very much a real instrument and produced in the same way as a standard trumpet. It has the same length of tubing and is pitched in Bb, however by winding the tubing much more tightly it is reduced to a more compact overall size. It has a cylindrical bore, so is definitely a trumpet rather than a cornet (see Trumpet v Cornet), but the bell diameter is much smaller than a standard one. This tightly wrapped tubing and smaller bell means that the air flow is more restricted than on a normal trumpet resulting in an instrument that is not as free blowing with a tone that is somewhat thinner.
You are unlikely to find a pocket trumpet in any traditional group such as an orchestra, concert or brass band. They really are a novelty instrument but can be good fun if used in the right performance environment. Technically they can be played in any ensemble that has trumpet parts but as mentioned above the overall sound quality would suffer.
They also have a more practical use which is for brass players going on holiday and looking for something that doesn't take up too much space in their car or suitcase. They are the perfect instrument for keeping your lips 'ticking over' whilst away from home. As they use a standard trumpet mouthpiece a player is able to take their normal mouthpiece with them to use whilst practicing on their pocket instrument.