Short answer: No, using a checking account draft doesn't save the fee entirely. It might be less than that of a credit card, though.
EE charges a flat fee for membership, test and event registrations. The organizing club usually adds a percentage "convenience fee" to cover that cost and some/all of the credit processing.
All online payment transactions are run through Stripe.com. The fees vary based on the type of payment (ACH vs Card) and/or card type. Amex charges the highest percentage rate, so many clubs simply don't accept Amex cards.
When payment is made offline via cash or a personal check, EE still charges their flat fee.
The system organizes some paperwork and data integrations, but memberships are still renewed manually on the USFS/ISI sites by the membership chairperson. They do have an export template that streamlines the updating of LTS USA but US Figure Skating doesn't have import functionality for memberships. Tests registration, scheduling and email approvals are tracked but the test attempts/results have to be manually updated in the US Figure Skating system.
For competitions, EE is really good - it lets the LOC (Local Organizing Committee) manage registrations, music uploads practice session purchases and event groupings. They have developed import/export formats to let EE exchange data with the music, judging and accounting systems used at the competitions. Additionally, EE has reports/exports that can be used for credentials, lists, verfications and other documents that require registration data. It can even provide an online "storefront" for merchandise sales like pins or shirts. It's complex, but much easier to use than the Event Management System that US Figure Skating uses for their events. (In my opinion.)
EE has some limited CRM functionality. Admins can email all the members who haven't renewed their memberships; LOCs can reach out to all coaches and skaters via email; test approvals go to whomever. However, it doesn't track those messages, so you can't see what messages were sent/received. That's why many clubs use another online tool for newsletters and communications.