Would like to know if the correct illumination module is necessary when I run the software on images for quantification of the levels of fluorescence.
The short answer is: Run the module if you feel that the illumination is in need of correcting to get a good result.
For example, if there is a systemic spatial heterogeneity present and you need to quantify fluorescence (e.g, Fig.1(c-d) from our Genome Biology paper), then correction is needed. But if the background intensity is fairly uniform across the image, correction may not be needed.
One case in which we always perform illumination correction regardless is if the imaging is being done in batches (e.g, a screen in multiple runs or across several days); in that case, you may need correction to handle how the optics/hardware changes during the per-run time course (e.g., bulb brightness).
We have a written tutorial on this subject on our webpage. Check it out!