My wife and I decided to prepare a pasta dish from a box (maybe we were both low on sodium that day) and the instructions said to heat for five minutes, then let stand for another five minutes so the sauce would thicken. After it had been standing for a minute, I stirred it to hasten its thickening. My wife said stirring it would have no bearing on the rate of thickening (“the package says ‘let stand for five minutes; it doesn’t say to stir it.”) I heard. I responded that she was taking the instructions too literally. I contend that the sauce thickens faster when it’s stirred every so often as that releases water vapor faster by exposing more surface area, as you can actually see the water vapor rise from the product. She disagrees. Without using a thickener, the only way to thicken a sauce is to remove water, and wouldn’t stirring accomplish that more quickly?
A boxed sauce will have a thickener already added to it.
Corn starch/water doesn’t rely on liquid evaporating to thicken.
I agree that stirring isn’t necessary to thicken when there’s a thickener. However, when making a white sauce from scratch, it’s important to stir constantly to keep the temperature consistent to avoid scorching and skin formation, among other things. For your box mix, you are probably not heating it to boiling, though.
When a recipe says “let stand” it means “let stand and don’t do anything to it.” 
Stirring wouldn’t have any appreciable effect on the thickening process. It will allow steam to escape a little more freely, but if it’s already boiling there’s no point to this, since it’s already venting stem well enough; it’s only useful (and marginally so at that) if it’s simmering on very low heat (no bubbling). Letting it stand will work just as well and would be less tiring on your arms. Stirring occasionally will prevent it from sticking to the bottom of the pot though, or in the case of cream sauces, will help prevent clumping (where cheese is involved) and scorching.
Most store-bought sauce already has thickener in it. Some store-brands (I’m thinking of Highland Farms’ brand here in southern Ontario) don’t though, and the tomato sauce tends to separate from the water after cooking unless you add some flour or corn starch. (I hate sauces that do that.)