How soundproof is roxul / acoustical putty?
It's impossible to say how soundproof an installation will be. We can make a reasonable estimate if we know all the details, including potential flanking paths. A wall of this type may give you an STC 45 or something (wild guess). But even if it were STC 300, you'll still hear a screaming child due to flanking paths. Just how much do you need to hear? You're not going to hear them plotting their first great escape, but if a child is in trouble, you'll hear about it, unless the stereo or TV is up fairly loud.