No, that's not the way it works in this patch. All SQL tabs are sharing the same output pane. At this point, the tabs only help organize code into files. For me, it's easier to switch tabs and hit F5 then keep highlighting the text to execute in the same query box.
I know that this is not a true and complete implementation of the tabbed UI for a database, but making a separate output pane for each query would require a lot more code changes. Also, you would probably want to be able to execute code on more then one tab in parallel, which would require a separate connection for each tab. (Although I can definitely see a benefit of having an output pane per tab even if they all share the same connection.) Personally, I tend to keep a lot of tabs open purely for code organization purposes and would not want to saturate the server with so many connections.
I might tackle some of the above points later, but seeing how I am not very well versed in C++ and that this is my first ever contribution to this project (or any project using C++ for that matter), I would prefer not to take on such big changes right away. On the other hand, I would be more then willing to collaborate with somebody on some of bigger changes, if needed.