Does this imply that short-run aggregate supply curves are independent of the level of investment currently existing in an industry?

No.

I'm guessing this is your argument: I buy fewer widgets, so firms invest less in widget factories, which changes the supply curve. But what's happening is you buy fewer widgets, which lowers price, which moves firms to a different point on their supply curve which has them building fewer factories.

This kind of thing is really easy to get confused about, and isn't important unless, as with the original post, you want to use supply and demand curves to trace out how you can move from one equilibrium to another.