Do they offer an api?
We (Fastmail) are set up for human-to-human emails rather than bulk mailing, so if you try to do bulk mailing you're likely to hit limits and possibly terms of service issues - if you're trying to do the kind of thing that people use mailgun for, then I'd recommend using something like mailgun instead!
https://fastmail.blog/open-technologies/jmap-new-email-open-...