I think that depends on the embassy you apply at. In my case, I intend to train on a weekly basis so I paid for a 9 month program in advance and will renew it again in 9 months. I'm not trying to game the system.
A simple letter from the gym will not suffice. The gym needs to be reputable and meet certain qualifications. My gym provided a 20 page document containing an acceptance letter, various qualifications, and detailed information about the gym and program. It's totally fine if the gym will sponsor your training for free -- but make sure they meet the qualifications and have sponsored DTV applicants in the past.