What Internet connection does the smartphone use? Mobile providers might not give public IP addresses or prevent running a mail servers in other ways. Sending might be blocked too (not all is: my server logs connection attempts from mobile ISP users), servers might blacklist all "consumer" IPs to reduce spam (Google and other big providers do this).
If you run GNU/Linux on your phone and have root access (e.g. a chroot on an Android-compatible phone), it should be possible to run the mail server. Many phones have modems with access to all RAM and nearly all phones have nonfree drivers running on the application CPU, they could read the mails or keys from memory.
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