Really the battery doesn't care about the position of the display at all. While the is certain things that aren't optimal for Li-Ion batteries (and keeping them at full charge all the time is one of them), none of those things really makes a big difference compared to just bad luck (or maybe bad batteries).

Does clamshell mode affect battery?

Apparently it doesn't damage the battery at all. Would it be fine if once I'm done using it, I disconnect the AC adapter?

Is it bad to leave your Macbook on in clamshell mode?

No it won't hurt anything. There are differing opinions on this. If you run on power adapter as much as possible, then you're saving "cycles" of which your battery has limited amount of. Age will also take its toll on a battery, no matter the usage.