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Great question Felise! I actually have this grand plan to not have any brown sugar in my kitchen, and to use granulated white sugar with molasses so I can dial in exactly the right amount of chewiness and/for flavor complexity I need according to the task-at-hand. You should theoretically be able to do it the other way around: with brown sugar and no molasses, but since I don't know the exact amount of molasses in 1 1/2 cups sugar, it would be difficult to see if it would work exactly the same.

The long answer: Basically, molasses is extremely important in chocolate chip cookies (and some other cookie varieties) because it determines the chewiness of the cookie and lends background flavor notes, not necessarily perceived as "molasses like". Molasses consists of long, sticky sugars that hold onto water, hence the gooeyness, so this would also effect the way your cookies spread during baking too. This is because as molasses holds onto the water, it's less likely to evaporate during baking, thus making your cookies remain in a liquid state longer. The longer your cookies remain in a liquid state during baking, the more they'll spread flat. So molasses is used to "tune" many cookie recipes for optimum flavor, texture and shape.

The short answer: you could probably get away with brown sugar but the cookies wouldn't turn out exactly as designed. Good luck!