I'm not 100% sure what you're describing, but the ability for one player to buy an item and give it to another basically means that ADC will want Support to buy nothing but the income item and control wards so Support can help ADC rush a build. Even if it's only virtually possessed but still held by the Stash user (such as ADC gaining the "given" item's stat bonus but not being able to build from it) they'd still use that to get twice the power spike at 1300 (Let's back for two B. F. Swords for +80 AD) and then later the Support's held item could be sold off to build Redemption or whatever later on. (Or if not able to be sold off, then Support would just be behind on gold for ADC's greater glory.)
Already, Magical Footwear and Perfect Timing are powerful and they're only worth up to 600-ish gold, being able to buy an item for another player would bring back memories of Kleptomancy before the nerf to klepto items' sell values. (Perfect Timing's sellback was nerfed, too, wasn't it?)
I do like the idea of a bag of holding in a pinch, though. Perhaps it could be something like one of your inventory slots, while empty, can be activated once to allow you to buy an item while away from the fountain shop? It'd basically save one back normally and allow for a save when something happens and you really need something right now (like Stopwatch or Guardian Angel or a Control Ward, perhaps?), and it would be code-wise the same as becoming Ornn for a moment.