Yes, by all means use it as it's free!!
15/32" is 12mm in my language. I threw together a smallish upright for my kids using 12mm MDF and as already suggested, if you use a few braces connecting the side panels at strategic points it will be plenty strong enough. You'll also have the added bonus of a much lighter cabinet!
Don't worry about not having plans for braces, just use a couple of offcuts that are at least 6" wide and attach them to the side panels using angle brackets.
Just make sure you make a nice solid frame at the base of the cabinet as this will hold it all together!!