The top generates the vast majority of the sound. The back and sides do add some coloration, or if you like, filter the sound of the top on the inside by having reflection characteristics of a certain type. That is the extent of what the sides and backs do. The backs and sides, by their dimensions can indirectly affect the top's resonance by influencing the air pressure variation inside the guitar's body when the top is vibrating (in effect, acting as sort of spring or dampener based on volume). The backs and sides are mostly there for structural reasons, but do have some effect, if somewhat minor compared to the top. Depending on who you ask, the top contributes 80-90% of the guitar's tone and volume. The rest is from the back, sides, saddle, nut, bridge, and a whole lot of other factors (in that order, basically). By top i mean the soundboard and the bracing, just for clarity.
I have never played an all spruce guitar. As I have said above, they have been made, and reports say that they sounded warm/soft, but the volume was low. It is not known how much of that was due to the spruce back and sides or how much was due to the overall design. Until some builder does again start making all spruce guitars, and people have had a better chance of examining that guitar, most of this will be an unknown.