Possible - yes.
Do you want it? Probably, no. Especially, SMTP. Better use something like Zeptomail (cheapest) for delivery.
You can still self-host the receiver.
Mandatory do-not-self-host-at-home notice: custom domain at skiff.com is free, iCloud+ Mail is $0.99 and Zoho is $1.25/mo.
For one instance of app, it’s possible to install it onto a single machine.
Things get tricky when you want to access the data from multiple devices. Even trickier, when several people want to access it. After a certain point, it’s easier to have a “cloud” solution. And since “cloud” is just somebody’s else computer, why not make this a computer YOU own?