No specific reaction comes to mind other than the general transfer of NaOH enolates to the organic phase.
I don't think by-products would be much of an issue. I am just looking into how to maximize the speed of such [substitution] reactions through minimizing required temperature and reaction time by choosing an appropriate PTC. When alkyl chlorides are in play, which they often are due to their low cost, the intermediate alkyl halide that is generated by the PTC will greatly effect reaction times and efficiencies. Using an alkyl chloride + iodide-ptc should be have similarly to using an alkyl iodide, except, with less side reactions such as hydrolysis.
I did recall reading up that Iodide in the right molar quantity can act as a cocatalyst, such as NaI with TBAB/TBACl/CTAB, etc. So maybe that is what is going on.
IIRC, Iodide was said to be a catalyst poison because if there is too much of it, it ties up the PTC making it ineffective because of how rapidly iodide can leave and reattach to the catalyst. Though I wish to understand the mechanics behind what makes it a poison vs a cocatalyst.