Yip, quite possible. Of course you will need to have a script which will be able to make sense of the input $1, there are a few out there.
To do it you will probably create yourself an email alias in the /etc/aliases file, something like this:
an_alias: |"/path/to/script.sh"
If you want to write the whole email contents to a file its even easier:
an_alias: /var/tmp/a_logfile.log
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