The answer is no, you don't need any formal qualifications to do the job - in truth most people in the business are self trained or trained by the manufaturers. Obviously you need resonable plumbing skills, sound electrical knowledge and decent understanding of electronic circuits, and the ability to do mechanical repairs/parts fitting. The hardest part of the job is fault finding, but these days the appliances are mostly electronically controlled and need specilalised tools to do the job. With Miele applinaces for instance, everything produced in the last 10 years can be accessed via optical link on a laptop and my guys could not do their job without their laptops.
I've not seen any courses specific to the industry, but then again I havn't really looked recently - I'm sure someone will do one. Like this!
All the best with it, the most important things you need are the abilty to want to find out what's wrong and to want to fix it, if you have those qualities, you will find it very rewarding
Cheers
Powelly