The extent of coupling between the folding of a protein and its binding to a substrate varies from protein to protein. Some proteins have highly structured native states in solution, while others are natively disordered and only fold fully upon binding. In this Letter, we use Monte Carlo simulations to investigate how disordered polymer chains grafted around a binding site affect the folding and binding of three model proteins. The protein that approaches the substrate fully folded is more hindered during the binding process than those whose folding and binding are cooperative. The polymer chains act as localized crowding agents and can select correctly folded and bound configurations in favor of nonspecifically adsorbed states. The free energy change for forming all intraprotein and protein-substrate contacts can depend nonmonotonically on the polymer length.