Can jellyfish improve the Black Sea ecosystem?
To quote the PI from the BBC article:

But, Dr Dabiri explained, the jellyfish were unlikely to be the &quot;primary ocean mixers&quot;.  &quot;Crustaceans - like copepods and krill - are likely the primary biogenic mixers, because there are so many of them,&quot; he explained.
&quot;But much of the open ocean is like desert,&quot; he added, &quot;and the density of these animals is unlikely to be sufficient (to cause mixing).&quot;

My guess therefore is no, jellyfish would not be sufficient to dramatically change the current structure of ocean layers.  Animals in general, as the paper and its references suggest, do contribute significantly, on-par with tides and wind.