Does the demand for bad quality products increase when there is information asymmetry?
In the second case (information asymmetry) there is only a single market. This may be the market for the product with unknown quality or in case of adverse selection it may be a market for the bad quality product alone. Assuming there is no adverse selection the reservation price of a consumer w.r.t. the unknown good is the expected value of his reservation prices from the full information case. Thus it is a weighted average and will fall between the reservation prices of the good quality product and the bad quality product. Since this is true for all consumers, the demand function adjusts in the way you described.

What happens exactly (number of products sold) depends on the market structure, whether the seller of the goods is a monopoly or there is supply-side competition.