No, I do not think that this website offers any legal guarantee on the licenses it certifies. To back this claim, here is what I found on this page http://copyfree.org/policy:
It is not the policy of the Copyfree Initiative at this time to use its certification process as an endorsement or review of the legal quality of a given license draft, nor any other standards of judgment beyond simple conformance with the principles embodied in the Copyfree Standard Definition. Plans are underway to establish recommended guidelines for license selection for interested parties, but these plans are not at present reflected in, or intended to be inferred from, any content of the Copyfree Initiative site. We hope that the presence of both the certified license list and the rejected license list serve your purposes for choosing licenses that conform to your general licensing policy preferences, though further information should be sought from other sources such as qualified legal professionals where appropriate.
This is somewhat like the list from the FSF http://www.gnu.org/licenses/license-list.en.html they comment lots of software licenses and say whether they deem them to be free or not. See for instance their comment on the WTFPL:
This is a lax permissive non-copyleft free software license, compatible with the GNU GPL.
We do not recommend this license. If you want a lax permissive license for a small program, we recommend the X11 license. A larger program usually ought to be copyleft; but if you are set on using a lax permissive license for one, we recommend the Apache 2.0 license since it protects users from patent treachery.
What they mean by "lax permissive non-copyleft" license is precisely what you are looking for: a "copyfree" license. They still agree that this is a "free" license but they discourage its use.
Going back to the list http://copyfree.org/standard/licenses it contains both licenses which can be considered "crayon" licenses such as the WTFPL (still quite a popular license) and the Beer-Ware license, and licenses which are very fine, and very recommended:
CC-0 and the Unlicense are public domain dedications while MIT and BSD require attribution. I would definitely recommend that you choose one of these four.
Note that the FSF argues for CC-0 over the Unlicense:
The Unlicense is a public domain dedication. A work released under the Unlicense is dedicated to the public domain to the fullest extent permitted by law, and also comes with an additional lax license that helps cover any cases where the dedication is inadequate. Both public domain works and the lax license provided by the Unlicense are compatible with the GNU GPL.
If you want to release your work to the public domain, we recommend you use CC0. CC0 also provides a public domain dedication with a fallback license, and is more thorough and mature than the Unlicense.