I am also not a lawyer, so take all this with that in mind.
As far as copyright goes, I guess it would be the equivalent of the "poor man's copyright" which is to say it would be equally ineffective. Copyright is secured upon creation of a work and, in the U.S., registration is required for full benefits of copyright protection. So, eMailing a copy to yourself isn't going to really assist in that.
Insofar as establishing that you wrote it and when you wrote it, well, maybe it might be useful. That is, if you can show you wrote it before someone else wrote it, you might be able to help establish that they copied you rather than the other way around.* Whether the datestamp on the eMail would be considered credible in a court of law, I don't know. Additionally, you would have to take eMail retention policies into consideration. The datestamp is only useful insofar as the eMail provider has a record of that eMail. If they've deleted the data from their servers and archives, there's no way to prove the datestamp you show on your copy of the eMail is correct because there would be no way to verify it against your eMail provider's records.
Laws regarding eMail retention vary. The average is three to seven years depending on who and what and why the eMails might need to be retained. So, let's say that they only retain records for seven years. If you're involved in a copyright infringement lawsuit within those seven years, there's the possibility their records could be subpoenaed to verify your datestamps. After that seven year period, you'd be out of luck.
Maybe one of the actual lawyers that linger around here can offer more accurate information.
*And note here that you have to prove that they copied from you, not just that you both had similar ideas and maybe you started on yours first. Can you prove they had access to yours, for example?
So, I don't know. It seems to be a lot of work to eMail copies of stuff to yourself all the time, and then maintain those eMails and datestamps and hope your eMail provider retains those records to be able to verify your datestamps if need be and hope if your work is infringed that it occurs before your provider has deleted their records and so on. And, if that work isn't going to be useful or valid in a court of law, you've done a lot of busy work that accomplished nothing.
The likelihood of someone stealing your stuff prior to publication is pretty slim. Sure, a hacker could get into your computer, but a hacker is probably more interested in your financial stuff than your writing. If you're concerned, you could work on a computer completely disconnected from the Internet.
Otherwise, once you publish, then your work is out there. That's when it's more likely to be copied. And if you publish something on Amazon tomorrow and someone copies it and posts their version next week, well, you can show that you published first. And if they copy word for word, well, you've got that too. They could try to claim you copied them, but then they have to prove you had access to their work prior to publication.
So, when you take all that into consideration, I'm not sure how much, if any, benefit there would be to eMail copies to yourself.