Crap in = crap out. But its not really that straight forward.how much does juice quality really matters within reason.
Store juice is meant for drinking, not fermenting. What I mean is, the blend of Store juice is primarily sweet and lacking the bitter and sharp flavor profiles. You can compensate with specific additions, but its still just a polished turd. (I make polished turd cider, no judgements here.)
Traditional cider juice made from specific blends of cider apples would not likely taste very good as juice, but make a very deep and complex cider.
You can make really good simple cider, just recognize its limitations. Think of it like a box of franzia burgundy or granache as compared to a fine French wine. Both are wine, both drinkable. In a blind test many would actually enjoy the box wine. But it is very "simple" as compared to its well crafted cousin.