Are you talking about human Sasori, or puppet Sasori? Human Sasori yes, puppet Sasori maybe. We have two great sides of this discussion. What we know about puppet Sasori, he has a "hart", and a viable chakra network. But as far as we know and understand no nervous system to feel or sense pain. But this leads us to another question just as problematic. Is Sasori even a sentinent being or just a puppet following a elaborate preprogrammed routine. (similar to a zetsu in a puppet)
From what we observe Puppet Sasori to emote to some degree,which requires some sort of cognizance unless it was a programmed but even said programing would need someplace to reside, thinking Sasori's core could contain more than just his chakra it could be his mind/hart as well. Thus making him susceptible to genjutsu. Assuming that you can find the core and disrupt its chakra flow. And if you could it would more than likely just cause him to short circuit, till the disruption faded or was no longer present.
So if anyone can define and pinpoint whether the "mind" resides in the brain or if it is based just in chakra as has been seen to do with black "Zetsu" (madara's will) and also Orchimaru's curse seal paradigm which suggests that ones brain need not be in a given area for ones consciousness/will to be there to observe and interact with a given environment. With that being said even if Sasori is using a similar process he would/should still be able to be affected by a given disruption to his chakra. With the Orochimaru curse seal comparison the only thing that keeps his curse seal in check is the hosts chakra, and "will".
Going with yes...he could be one way or another affected by genjutsu. Deception is a shinobi's weapon, if Sasori says he cant feel pain he might be right but theres more than one kind of pain blah blah...