A fatter neck might help the sound in some cases, and hurt in other cases, or it might make no difference at all. How's that for a definitive answer?
Seriously, we usually talk about the sound of the guitar being influenced by the resonant modes of the top, or the back, or the air in the body, but the neck can play a part too. There's a resonance of the entire guitar, where it vibrates like a xylophone bar in it's fundamental mode, with stationary points near the nut, and across the lower bout at about the wide point. This is often called the 'neck mode' because the neck bends a lot when the guitar vibrates like this, but it's really the whole instrument shaking.
Normally, this mode is well below the pitch of the 'main air' resonance, which is the lowest mode that can effectively produce sound. However, if the neck is particularly stiff, and the headstock is light, the 'neck mode' resonance can be as high as the 'main air' pitch, and then the two can work together. The result is that the normal 'main air' peak in the spectrum of the guitar is spread out a bit, showing up as a pair of lower peaks with a dip in between. The 'total available horsepower' in that range is a bit greater, and, because you don't have one tall peak, the sound is more 'even', with less chance of a 'wolf' note. Often guitars that have this sort of couple will have a particularly 'dark' or 'rich' low end.
It's usually pretty easy to hear the 'neck mode'. Hold the guitar up by pinching the neck between your thumb and finger loosely up around the nut. Let the guitar hang freely, and be sure to damp the strings with you finger. Tap on the back of the headstock with a finger tip, and listen with your ear as close as possible to the headstock surface. You should hear a low, pitched sound, often around C=65.4 Hz, well below the low E string pitch.
It is possible for neck vibration to 'steal' energy from the strings, but I think there's a lot less of that than most people believe, at least on acoustics. For this to happen really effectively the pitch of the note played would have to closely match that of a resonance of the whole guitar, like the 'neck mode', and you'd have to be fretting that note near an 'antinode' of the resonance: one of the places where it moves the most. The 'neck mode' I've talked about is the lowest pitched resonance of a whole family of modes, but the next higher one is usually 'way up; nearer 300 Hz, iirc. The pitches of the higher modes varies a lot.
On a solid body the neck is lot bigger part of the thing, in a sense. Also, they're trying to do just about the opposite of what we acoustic makers are trying to do: we want the bridge to move, they want it to stand still. I have noticed on some solid bodies that the node lines for the lower three or so resonant modes (the ones that are low enough in pitch to be fundamentals of played notes) all tend to be near the bridge. This means that, unless you happen to hit an antinode up on the neck someplace, you're unlikely to be able to drive any 'wood' resonance very well, and the body won't be stealing energy from the strings. I imagine the node locations, and the pitch of the various modes, varies a fair amount depending on how stiff the neck is, and how heavy the headstock and body are, so the neck could make quite a difference in the sound.
Electric basses are a good example of what _not_ to do, IMO. They put the bridge right down at the lower end of the body, which is an antinode for _every_ resonance of the stick. There are bound to be frequencies where the bridge is moving, stealing energy from the strings, and that's why solid body bases are prone to 'dead notes'. That bridge location makes sense from a lot of standpoints, but not from that of sound.
*wonders just where this leaves us No brainers * ![[uncle]](./images/smilies/surrenderflagqv6.gif "Uncle")