This teacher training that various people offer is called TEFL - Teaching English as a Foreign Language.
It is more of a confidence booster / builder and organizational tool to help you be more prepared and efficient when teaching.
Yes. Experience teaching business English or having an awareness of what would be considered Business jargon helps a lot.

There are at least 2 kinds of teacher training in Madrid. TEFL and CELTA. ITC, EBC, Canterbury, Windsor / Trinity offer the TEFL. I am not sure who else.
International House offers CELTA.
Other schools out here are Advanced Institute, but I am not sure what they do.
You can also check www.tefl.com for some more info.

ITC - Based out of Prague. Have Training Centers in Prague, Barcelona and Madrid. Only guarantee jobs in Eastern Europe. Offer job guidance everywhere else.

EBC - Based in Madrid. Grew out of their already existing Language Teaching Service. Offer job guidance. Will put you at the top of the list when the parent company is hiring language teachers.

Canterbury - Based in Madrid. Grew out of their already existing language academy. Used to only guarantee jobs and therefore limit the number of students, but have recently added a 2nd more cost effective option where you can just get the certificate and move on or find your own better jobs after.

Note: In Madrid there is so much of a demand year round for English teachers both legal or not that you will do better finding your own jobs for 10 euros to 15 euros an hour instead of the 9 euros an hour that anyone can guarantee you.
The rest I am not sure about, but would like to know more.
Windsor / Trinity - ?
International House - CELTA ?
Advanced Institute - TEFL ?
Rocco.