It doesn't work. It hasn't worked as evidence in U.S. courts since sometime in the 1920s.
"Poor Man's Copyright" is not an area of law or a concept that exists in law. It is a term non-lawyers have attached to evidence authors create to prove their authorship, because they are afraid the authorship of their work may be disputed. This rarely happens, but is, nonetheless obsessed over by unpublished authors.
Copyright protection vests as soon as the work is created. Nothing has to be registered to confer ownership of the copyright on the owner. In the United States, every "poor man" who creates something automatically gets the copyright.
In the very rare case that somebody steals an unpublished work, and then claims to have written it himself, evidence establishing the author's possession of the work on a specific date before the plagiarist claims to have created may be probative to establishing the copyright owner's authorship, or to disproving the claim of a false author.
It is difficult to imagine this kind of evidence being probative to any other sort of dispute. I suspect most copyright lawsuits brought by unpublished authors are met with defenses that the alleged infringing work is coincidentally similar in some respects, but does not infringe the plaintiff's copyright. In this case neither "poor man's copyright" nor registration is pertinent to the central factual question of whether the allegedly infringing work actually infringes the copyright.
However, if an issue of disputed authorship has ever gone to trial, then evidence of authorship must necessarily have been introduced, weighed by a jury, and used in making a determination.
Mailing yourself a copy of the work to prove that you wrote it is not a substitute for registration, because registration confers certain rights on plaintiffs, including statutory damages. However it shouldn't be a big deal for any author to prove he created his work, through draft versions, preserved locally and on remote servers, through a history of submitting the work, and through the testimony of witnesses who saw the work and can corroborate the author's version of the facts.
A case where the author's sole proof of authorship was a registered letter he sent to himself would likely fall through. Moreover, many authors who create such evidence as a safeguard may later believe it establishes something pertinent in a case where the date of creation really isn't at issue.
But there's no reason I am aware of that would prevent any evidence of authorship from being presented to a jury. As to whether a registered envelope would be easily impeached by arguments about tampering, I'm really not sure. It seems likely such evidence could be discredited. An e-mail would probably stand up better. I don't know of any way to falsify the time stamp on an e-mail through a service like Gmail.
Saved drafts timestamped by a remote computer would be stronger evidence than saved drafts timestamped by a local computer, because you can modify the timestamps on local files. I always email my work to myself so I can revert to older versions if I change my mind about something, and to preserve the work in case of computer failure.