Nope; fiberboard, celotex, homosote, etc, all too low mass to be a good idea. Plywood would work better, and it's still not as heavy as gypsum.
If you cant/don't wanna use corner bracing, for an outside wall structure I'd put up the heaviest plywood/OSB you can afford, put your favorite siding over it, and plan on a second inner frame with several layers of gypboard.
If people are building from scratch, it's not practical to re-invent the wheel - if you stick with proven methods, and do them right, you'll get predictable results. When you start wanting to try compressed monkey-doo, fried marshmallow, straw bales, etc, you're pretty much on your own. No one here has (or can afford) the kind of lab environment and man-hours it takes to properly test odd-ball materials.
I know we get into some pretty esoteric stuff at times, but the only time I consider that necessary is when someone is trying to "turn a sow's ear into a silk purse", so to speak; it can be very daunting (as most of us know) to convert an already existing space, one that was built with no intent or knowledge of sound isolation) into something that works. That's when it's usually necessary to get creative, NOT when you have the golden opportunity to build from scratch.
Anyway, when trying to figure out what to use (new construction) it's really very simple - for outer layers, you need structural strength and moisture resistance. Find the thickest, heaviest material you can afford that meets those requirements, and hang it on your outside frame - follow the recommendations for gap spacing (you'll be sorry if you don't) for that specific material, then caulk those gaps for a flexible, airtight seal. Cover with whatever siding you decide on, preferably one that does NOT leave gaps (like hardi-plank or other "lap" sidings). This will be your outer leaf.
For inner surfaces it's easier - in the US at least, gypsum is king. Period. Only exception I can think of is if you are a mason. People who envision wanting to hang stuff on their walls have good results putting a layer of MDF under the last layer of drywall. Put several layers on the inner frame, no seams coincident, either hire a pro drywaller who will LISTEN about decoupling or learn to do it yourself -
this
will tell you more about drywalling than you ever wanted to know, although even it is pretty light on sound construction; but you can get that here
Soooo, any-hoo, for the 4704th time, use the heaviest cheap (or cheapest heavy) stuff you can find, seal it, leave an insulated air gap (larger is better, up to 3 feet if you can afford the space) and do it again. Rather than repeat ALL this again, please re-read the REFERENCE section -
And when you're shopping for wall panels, try this - rest the panel on your foot, right where your toes curl up when you eat your favorite pizza; if it doesn't hurt, it's not
HEAVY enough

Steve