yes, you could. I'd probably install a small linux distro. But you should definitely read up on mail administration and if you use this for other people (or want your own email to be reliably available) you would need to look at backups and some form of redundancy.
You should also look into your ISP terms of service to make sure it's allowed.
Also get a dedicated connection with a dedicated IP, not one that frequently changes or periodically changes via DHCP to your DSL/Cable modem.
You'll also want to read up on your spam filtering and security; if your system gets hijacked, you'll become a relay for sending spam. You will want to familiarize yourself with outside websites that will test your system for common misconfiguration issues.
If you're completely new to system administration you might not realize just how difficult it can be to properly administer an email server...