can you grow "store-bought" garlic?

Hi yes is the answer...........I did just that in October with some store bought ones I brought back from the Gers region in SW France & already there's about 12" of green growth, plus, the "bulb" is looking pretty good too.
Go for it

I believe if you pull off the cloves and plant them individually they will all sprout into plants.

As I understand it, the store-bought ones are likely to be varieties which have been bred for 'industrial' production and so might not perform too well in the average garden - but yes, they will grow and the smell of fresh garlic . . . !