I don't have a Theravada perspective, just some background:
Eshin Godfrey Oso is a ZFI member and uses koans. There is an interview with him here:
http://www.sweepingzen.com/Eshin_Godfrey_Interview.html
In Chan and also Korean Zen (Seon) they often used hua-tou (hwadu) which is like an abbreviated koan. Common examples are "What is is?" and "Who is doing this practice?"
But the right approach to doing this practice is subtle. From what I understand it's like a gentle but relentless inquiry that becomes a 24/7 affair, accumulating ever more energy until everything else pretty much falls by the wayside. It is essentially a form of meditation having both samatha and vipassana, as the practitioner concentrates to the exclusion of all else, with a subtle sense of dukkha (Great Doubt) driving the inquiry.
Here's some instruction from contemporary teacher Hsu Yun, there is also quite a lot on the koreanbuddhism.net site:
http://hsuyun.budismo.net/en/dharma/chan_sessions2.htmlBut frankly I don't see how these practices can be meshed well with Theravada. Even the terminology (Self, Buddha-nature, etc) will rub people the wrong way and produce lots of misunderstanding.
_/|\_