I think you're misunderstanding what a copyright does. No, a copyright is no substitution for a patent, in any way, shape, or form.
I posted an answer a few months ago on Startups Stack Exchange which roughly describes the difference between these two mechanisms of intellectual property protection, "Can you copyright a program you have made from scratch?" Clearly, that question is asking about code, rather than antennas, but the same theories apply nicely here.
What that disclaimer ("COMMERCIALLY AVAILABLE...") is referring to is the plans. Looking at their designs as an amateur radio operator, I'm not seeing anything that looks to meet the bar for patentability, but I'm especially not seeing any patent numbers, or even "patent pending" footnotes.
Copyrights are not on-topic for Ask Patents, so I won't say too much here (although I will urge you to check out the answer I linked to before), but essentially, the protection this website is getting is on the graphics, text, and related artwork they've used. By law, copyrights aren't on anything useful--they're just for artwork (text, images, songs, movies, dances, and such). If I opened my own antenna store, basically, I wouldn't be allowed to copy and paste these images to sell this kind of antenna.
What they are not protecting, is the antenna itself. In this hypothetical store, I would be allowed to sell the type of antenna, indeed with even the same measurements.
It's true that by publishing these plans, they are barring someone else from getting a patent on the same antenna, although in this particular case, as I said, it's unlikely that anyone would be able to get one anyway.
Speaking to your general questions, they really depend on how you define "design."
I'm seeing two possible definitions, to which the answers would vary:
- The design of the plans.
- The design of the antenna, in this case.
In the first case, nope! The copyright is still theirs, so they can stop someone else, as I've described, from using the verbatim scripts on their own website.
In the second case, it depends! The quote you cited does refer to the United States grace-period of one year, which is relevant here. It is, however, true that once you publish your work publicly, you stand the risk of someone else getting some valuable market time before your patent goes through (which can take a little while). You'll be able to stop them once your patent does come through, but sometimes that's too late. Marking your invention "patent pending" is really the best form of protection in that early stage.
So ultimately, no. A copyright is not any form of protection towards the underlying utility of a product.