I downloaded the paper you mention, and it answers "no", at least at the publishing time of the paper. That's for two reasons:
a paper is required to properly review related work, and they do so in the introduction, with a summary in Fig. 1, which says "no". At least if it has been published in a reputable conference, but it looks like that (Brodal is cited a couple of times in "Purely functional data structures" by C. Okasaki, a reference on the subject).
However, they mention in the text an algorithm with search time O(log n log log n) and concatenation in O(1) time, sketched in the K&T paper from STOC '96. It might be interesting for you.
- the open challenge by K&T that they solve is about dictionaries with O(1) concatenation and O(log N) search/insert/delete, even for ephemeral structures.
Point 1. also ensures that you can simply look for papers citing this one to find any later results, they would need to cite it.
If the question were of practical relevance (but it is not supposed to be), I believe that constant factors are more important than the difference between O(1) and O(log N) (as discussed in Sedgewick's Introduction to algorithms), so you need to look just for benchmarks for the use case of your application.