No, the face shield on that respirator is for fumes and chemical splash protection and not for impact protection. Don't count on any face shield being able to provide adequate protection against impacts by large high speed pieces of wood. There are several categories under ANSI Z87.1, but they all are for eye protection against fumes, splashes, dust, or small objects.
Other safety precautions such as checking the integrity of the wood, the holding method, lathe speed, tool rest position, correct tool, body position and cutting technique need to be part of your first line of protection.
If launching pieces off the lathe is something that you do occasionally, it is worthwhile to consider wearing head gear in addition to figuring out why this is happening.