No. You can also use your own SMTP providers (Amazon SES, Google, Mailgun, SendGrid, etc.) or use a completely external solution (like Microsoft Exchange or Google Mail, which we obviously do not recommend). If you do so, send us an Email to support@happyhosting.co with the required DNS entries and we'll set it up for you.
But: our internal mail server automatically sets up SPF, DKIM, and DMARC for you - giving your mails a perfect spam score.
For a detailed overview of the available options and differences of the outgoing mail-solution, check out this article.