At the risk of semantics, I suppose it comes down to what it means to provide child support. If I had a child support agreement to buy a car for my ex partner and that was to reduce my child support by 100% and then I took the car back off her, it wouldn't exactly be providing child support. Its probably a bad example though, as surely she'd be demanding the car be registered in her name! A better example may be an agreement that stipulates one party pay child support by covering the other parties share of the mortgage payment prior to property settlement. That doesn't increase the payer's share of the asset, they are making a payment to the payee, by virtue of paying a third party. If they were to redraw any of these payments, surely the payment has not been provided. I think that's the closest example I can think of.
I think the safest thing to do if you were drafting one of these would be to include them as periodic amounts, e.g. dad is to pay an additional $x per week and mum will use that to buy books/uniforms. I can find a few case law examples of s124 orders made under the Assessment Act, but those are just ordering that a party pays for the uniforms, no definitive answers on who owns them. I might be better off looking for enforcement proceedings at the FCC or FLC, but there aren't a lot of those around (and the cricket is on)