OG Mailinglist works well with Mailgun backend. Just make sure you set correct API key, username and password on admin/config/group/mailinglist configuration page.
Reducing Mailgun load
Mailgun counts both incoming and outgoing emails. To reduce this, one could send email from the server and only use Mailgun for the incoming emails, which for largers mailinglists is just a fraction of all outgoing emails (someone please clarify if Mailgun counts email going to group as single email or counts all the recipients as well).