Yes, but they left Stern an out in the way they ordered the testing. Now he has filed the appeal, the Bahamian Court of Appeal can find the test was not admissible and they can vacate the order for the swab and order it destroyed at the lab in Ohio.
There is no "order" it was "directed" by the judge.
I have no idea why he showed up for the swabbing.
and yes he has the right to appeal, this why they scheduled the next court date for 2 weeks to give Stern his legal right to appeal. (lawyers in the Bahama said that the appeal would be denied because he was simply direct to do it - basically he did not have to show up - but remember he probably choose to because of everything else weighing in on him - the Florida stuff had not come out yet and then he had the Bahamian inquest coming up - after the Florida crap came out he appealed the Baby DNA test within a few days) But the end result is that Stern showed up for the swabbing so this means he agreed to the "direction" of the judge.
(The word "ordered" is what our US media chose to use, but there no such thing as a "order" for DNA tests in the Bahamas - it is only directed by the judge)