From a measurement stand point cytokine production is unregulated differentially with time. You need to know the time interval between stimulation and peak production for the cytokine you are interested in analysing. Stimulation for 4 hours should be sufficient but do the experiment and validate the results. The attached manuscript may help.
I suppose you CAN do it, but I would suggest that you simply bite the bullet and do it the way it is done in thousands of other papers. If you don't, you can't really discuss your results within the context of other findings. I realize that may sound harsh, but methods are important. What Mr. Gelder says is also useful. If I were reviewing your publication, I'd question it.
I have done something similar to what you suggest. Instead of washing the cells, however, I move the entire plate containing the cells, media, stimulants, etc, into 4C. The cells stay quite viable and retain the cytokines in my panel. All my work is with human primary cells. Before I adopted this protocol, I extensively tested and compared the conditions against processing the cells directly after incubation. You have to convince yourself, and others, that you haven't lost sensitivity or taken a hit in resolution by storing at 4C prior to staining. There are several Nature Protocols and Cytometry publications that allude to proceeding in this manner. Check for publications by Drs. M. Roederer and H. Maecker. Test, test, test, and make sure you can back up your protocol to others.
Agree with Cindy - in my lab we often do a 6 hour stimulation (either pathogen-specific antigens or non-specific activation like PMA/ionomycin), then transfer the cells directly from the incubator and leave at 4oC over night. The staining can be done the next day. We do this routinely on frozen and fresh primary human PBMCs looking for phenotypic markers and cytokines.
Of course, it's a good idea to validate this method in your hands (as the other commentators have said).
If you are staining intracellular cytokines, what you can do without any real hit on your results is to take through to the fixation point (for example, stain with CD4 and then fix the cells prior to permeabilizing them) and then you can store them in the fixed state overnight until you are ready to do the intracellular staining, flow cytometry etc. As the cells are fixed (with the CD4 antibody on them) you retain just the cytokines expressed during your experimental period.