Is Peach a competent leader.... hm... one could easily say she isn't....
In the "mainstream" series she doesn't appear to be very bright, letting herself be deceived by whatever poorly disguised plan Bowser comes up with (cake, anyone?). She is just very lucky to have Mario around who fixes almost every problem that arises. Without Mario, the whole kingdom would probably most likely collapse eventually.
However...
In the RPG series, she is usually quite capable and smart. While she still gets kidnapped rigtht and left, she actually manages to do something in these games, plays very important roles, is at points vital for Mario's success, and generally puts her damsel-counterpart from the other games to shame. In the RPG's Peach is actually one of my more favourite characters because of that.
That said the reason for Peach's reputation of being incompetent lies in Shigeru Miyamoto, since he said once in an interview that he is trying to keep Peach's personality at a minimum, thereby effectively turning her into a gullible damsel-in-distress by default to ensure Mario never loses his job.
A quote I once read about that subject springs to mind, that makes a good summary for it. "Mr. Miyamoto likes his women shallow and gullible."
So, to actually say something regarding the actual topic, I'd say "Yes, she is" in the RPGs and "No, she isn't", in most of the other games.
Remember, this is an opinion. Don't end up hurt by anything that does not conform to your views, as everything in there is subjective.
