When I talk about putting the character on-model, I mean that your drawing should look like the character you are trying to draw. Otherwise it will probably end up looking like some long lost relative. Having reference readily available makes your job that much easier. At least then you are not trying to draw completely out of your head, and we all know how hard that is.
For my comix I usually have my characters already established. I always have my model-sheets at hand so I can quickly reference any of my characters. Sometimes I go off model in my comix. This sometimes happens because I am still developing that character.
If you are doing a parody comix, then you should definitely use established reference material.
I have been thoroughly impressed with the Doshini that comes out of Japan. Those drawings are their own versions of what we here in America call Parodies. It is evident that those artist worked diligently in recreating their favorite character in a compromised situation using established reference material. There is of course some artist that have fallen short of making their parody version look exactly like the real version.
I cannot stress enough how important getting reference material is. Every professional artist out there already knows this and they make it part of there artistic expression. If you want to parody something, it is best to know what you are going to parody in the fist place. To do that, you must know your subject. How do you get to know your subject? Reference material.
P.S. Using my drawings/parodies as reference material will not help you get the character on-model. Even I am prone to making mistakes.
Jab