Email has several retries. Something like 6hr, 1day, 2days... After that the sender receives a delivery error.
All that is managed by the SMTP servers and the numbers change, but normally just losing internet connection or power for some hours doesnt make emails dissapear. By design.
While I have a cellphone, and can and do use it as a hotspot, I wouldn't exactly say it could provide a fallback connection for a server in my home, because it usually spends a significant part of the day out of WiFi reach of my home.
MTAs will retry delivery for up to a week. There are other options for more advanced usage though, e.g. one can configure multiple mail servers with different priorities, `the helm` having the highest priority and if it's down a MTA would try the next mail server which could be just a forwarder like mailgun.
Odd that they hide their FAQ in the shop page and hidden below the fold on a 13" screen. I looked everywhere but there. You'd think you most customers would want their questions answered before buying.