Yes it is possible, log4net supports an smtp appended that can be used to email logged events. If you look in the log4net.config file in the root of the web you'll see information in comments about how it can be configured. Note that if you customize the log4net.config file you should keep a copy of it as log4net.backup.config so you can restore your customizations easily after upgrades.
However, that said, it will probably be very annoying receiving that many emails. I know my log is very noisy with things poking at the site and mangling url fragments together resulting in lots of page not found errors. I find it easier to just review my logs several times a day and I clear the log after each time I review it.
I'm actually working on support for logging to the database as part of my effort for web farm support.
Hope that helps,