Overall shell construction does have an effect on the sound of a drum. Thin vs thick, multi ply vs stave/segmented/steam bent, additions of re-rings, bearing edge design, light or heavy hardware, thin triple flange hoops vs diecast or wood, etc. These things all play a roll in the overall sound of the drum. Heads, however, are going to be the thing that stands out to many as the determining factor for a drum's sound because it is the thing that is vibrating not only the most, but with the greatest amount of energy when the drum is struck.
Heads will have a large effect on shaping the overall "tone" the drum has (this is what most people hear when they hear a drum), but the shell, its design, and the various components attached to that shell all play a roll on the tambre of the drum (these are the tiny details that fall under that initial "tone" the heads have).
Now, these tambre differences can be very subtle, and many people won't really notice them. In many ways that is good because ignorance is bliss and cheap drums are awesome (it gives you more money for cymbals). I will fully admit that my ear is not so perfectly tuned in to hearing all the tiny differences in a drum's sound, but I can hear the difference between my Birch and Maple shells despite them both being made by the same company with the same shell construction and hardware. The drums can be tuned the exact same with the same heads, but the clarity and purity of the sound is different between the two. How the different frequency ranges are emphasized within the sound spectrum is different between the two. It's not the heads that are shaping these sounds, it's the shells. In contrast, I could not hear a difference (or at least not an appreciable enough difference) between my DW Collectors kit and my PDP Concept Maple kit with fresh cut edges. So the DW's were axed. Nice drums, but they didn't perform any better (for my needs) than their cheaper cousins. So win/win for me as I got to have a great sounding inexpensive kit and spent the extra money on great cymbals.
The "marketing" that many people talk about as being hogwash is mostly deserved, but if you spent all day, every work day, listening to drums of all different sizes and constructions you would start getting your ear tuned in to hearing the tiny nuances that each of the different drums and components have. These are the tiny, subtle things that set those particular drums apart from the rest. When everyone in the business is building round cylinders with a mylar diaphram on each side, you have to get in to the nitty-gritty detail of things to find what separates your product from everyone else's. Sometimes that difference is blown out of proportion, sometimes it is not.
In the end, heads make a big difference in the sound quality of your drums, but it is not the only factor.