Depend's on the equipment. The Forces will give a stipend to those who want to buy their own combat boots, for example, as the procurement system doesn't have enough to go around. At Wolverine, I could see them picking up safety glasses, rifle straps, and other accessories. I wouldn't expect them to be buying a backup weapon, as that would be highly regulated.
As an aside, I wonder if the Forces would be interested in purchasing a few WK181-C rifles, for use in opposing forces training exercises where you need live fire from 7.62x39 mm armed opponents? I'm sure they've got some sample AKs for this at bases, but I'm the Op Force would likely love a 7.62 rifle they could throw their C7 accessories on.