Even though the answer to your question is "no", many lawyers will advise you to add the copyright symbol anyway. Even if the symbol is not operative by law, it still operates on the minds of potential copyists who don't know whether it matters. In this regard, the copyright symbol is kinda like the "protected by ADT" sign in a front yard: It's not protection per se, but it might serve as a deterrent.
On the other hand, the likelihood that a mere copyright symbol will deter economically-consequential copying from a website/webapp is quite low. Therefore, as a former founder and current law student (and definitely not a lawyer yet), I'd advise you to do whatever the hell makes sense for your business for ancillary reasons. Add the symbol if you think you're dealing with superstitious folks to whom a copyright symbol lends an aura of credibility; omit it if you are going for a clean aesthetic.
Speaking of lawyers, unless a person is prepared to lawyer up, asserting copyright is largely empty. Litigating copyright takes time and money and energy. In typical infringement, the possible rewards will be blood from a stone scale. There are exceptions of course, but they don’t usually involve “the principle of the matter.”
Important to clarify that the answer is 'No' not because it is somehow an invalid way of marking copyright, but rather because it's not necessary.
You, as the author, automatically have copyright for your own creative works. No registration, marking or anything else needed. It also doesn't matter whether you share it or not - copyright is an automatic right.
Personally, I often use the footer (old, missing, sketchy name, giant company for niche market) to ignore a portion of vaporware/market tests without having to interpret any marketing babble..
Lawyers exist to get paid. We all know, for instance, that copyright notices in source code are pointless (and I mean like an extensive message in every single file) but it's more important for a lawyer to cover their ass from any possibly liability than to make the company more efficient. And of course, it creates work for them.
That's true for copyright notices in comments that get stripped out in compilation where the source itself isn't released. But a copyright notice in a no-op variable, or otherwise embedded in the distributed code, can help win a lawsuit by directly proving copying (which can sometimes be a nontrivial effort).
Text in distributed executables helped win a case for Apple back in the 1980s: "James Huston, an Apple systems programmer, concluded that the Franklin programs were 'unquestionably copied from Apple and could not have been independently created.' He reached this conclusion not only because it is 'almost impossible for so many lines of code' to be identically written, but also because his name, which he had embedded in one program (Master Create), and the word 'Applesoft', which was embedded in another (DOS 3.3), appeared on the Franklin master disk." Apple Computer Corp. v. Franklin Computer Corp., 714 F.2d 1240, 1245 (3d Cir. 1983) (Emphasis added.)
Work for the lawers? In my experience, it creates work for the developers, who maintain the automated license checks; rejects changes missing the nessasarry copyright; deal with files that cannot have a copyright notice for technical reasons; notice when they want to merge in a file with an incomopatable copyright.
My understanding is that registering with the copyright office and adding the goofy footer makes it much easier to sue for statutory damages, which can lead to a payout several orders of magnitude bigger than a lawsuit for "actual" damages
Someone copies a source file, maybe you can argue that it’s accidental. Someone copies a source file and strips out the copyright notice, that shows intent.
It takes an argument by a lawyer in front of a trier if fact before stripping copyright from source files shows anything. Irrespective of details, the wherewithal to lawyer up is mostly what matters because “fuck you sue me” is a sound legal strategy in so many cases. Or to put it another way, unless you have a lawyer on retainer the odds of bring a ne’erdowell to heel are low and one on retainer is probably saying it’s not worth it if they’re worth their salt. YMMV
On the other hand, the likelihood that a mere copyright symbol will deter economically-consequential copying from a website/webapp is quite low. Therefore, as a former founder and current law student (and definitely not a lawyer yet), I'd advise you to do whatever the hell makes sense for your business for ancillary reasons. Add the symbol if you think you're dealing with superstitious folks to whom a copyright symbol lends an aura of credibility; omit it if you are going for a clean aesthetic.