I assume of course, volume settings make no difference?
No it wont. The .gif file format is incapable of audio.... in the same way that .txt files cant display images.
.gif was specifically designed to be small file size - it does this by compressing the image and using a maximum of 256 colours.. which is why its not much good for photographs. Animated gifs (89a) are just a series of images strung together in a loop.
It really is just an auditory illusion.
It
may be possible with some trickery to make .gifs appear to have sound... but it would involve changing settings on the remote server to parse say .avi as a .gif... in the same way it's possible to get php to parse .htm files. Not sure if that would work with .avi as I havent looked into it.
I suppose you could also with CSS/html5 get a hidden sound file to play simultaneously, to make it appear like a .gif has sound.
Either way it depends on server side stuff and as soon as you download the file to view it locally the .gif will either just be a plain image... or it will simply fail to open as an invalid file extension because programs designed to open .gif files (eg photoshop) wont be able to read the headers.