Will a three-pronged plug adapter protect me against electrical shock when I use it in a two-prong receptacle?

Only if the wall plate screw is grounded.

Check your state and local codes before starting any project. Follow all safety precautions. Information in this document has been furnished by the North American Retail Hardware Association (NRHA) and associated contributors. Every effort has been made to ensure accuracy and safety. Neither NRHA, any contributor nor the retailer can be held responsible for damages or injuries resulting from the use of the information in this document.