It really depends on which Corps you join! Once you have completed your basic training, you will then go to one of the phase 2 training schools. If you join the REME, then this will either be SEME Bordon or SEAE Arborfield. SEME has an average team, but SEAE has a strong team.
Most years they win their local league, the Craftsmans cup, the 4 Divison cup and do well in the Army cup.
That being said, you cannot join a Corps purely because they have a strong hockey team, but the REME will give you a vocation that you can use when you get out, as well as a faster promotion rate than most other Corps.