They are too tightly packed so they are not going to survive that long. You could try separating a few plants out and pot them individually. Basil is in fact quite a big plant. [2ft x2ft]

That's what I did last year and they did quite well but would have done a lot better if we'd had a bit more heat - or a greenhouse.

Supermarket herbs are prepared and grown differently due to the huge amounts needed and they basically begin to die as soon as they are picked for the shelves. Therefore you are highly unlikely to have any success groing them from a supermarket bought plant. Grown on a sunny windowsill from seed they will grow quite quickly and can then be moved outside if prefered. I do this and then plant them into hanging baskets. They smell lovely as you walk past.