This could be a good idea , the PKK seems to be led by some serious boneheads .
Hw popular are they where they operate?
I wouldn't say that the PKK are led by "boneheads" and they are popular and somewhat respected as well, but it varies (of course). The thing to remember is that the PKK has fought for an independent Kurdistan for a
very long time and fought against not just Saddam Hussein, but also Turkey, Syria, and Iran (both under the Shah and Ayatollah).
They are basically left-wing nationalists, similar to the PIRA, FARC, or ETA. Turkey is probably right that the Kurdish authorities in Iraq have been soft on the PKK, in the same way that the black-led Mozambique would provide shelter for militant black groups that opposed the white minority governments in South Africa in the late 70's and 80's.
It is complex for the United States because in the past we have supported the Iranian and
likely the Syrian elements of the PKK, not so much because we believe in an independent Kurdistan, but just to disrupt governments we do not like.
It should also be noted that Turkey's human rights record, despite their being our allies in the Cold War, is not good and the Kurds in Turkey have not been a well-treated minority by any facet of the imagination. That is not to say that the actions of the PKK are tolerable, but that there are two sides to this story.