No, thankfully! Also, it appears (haven't gotten that far yet, myself) that one can choose whether one goes to Black City or White Forest, regardless of which version of the game.
Well, both start out with their version of the respective locations (Black City in B2 and White Forest in W2). However instead of people you battle or who determine what wild pokemon are available, you have battle tower-type places, either Black Tower in Black City or White Treehollow in White Forest. If you beat the first 5 areas of either, you unlock a key you can swap using Unova Link in the start up menu. Using that, you can switch between whether Black City or White Forest are available in BW2.
If I get there before you do, I'll let you know! I'm not doing what I normally do and devouring every spoiler I find, so although I'm not carefully avoiding all spoilers or anything, I haven't stumbled across "how that actually works" yet.
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