Is synecdoche a form of metaphor in which the part stands for the whole?
Yes. It works both ways.
Synecdoche is a figure of speech which expresses either more, or less, than it literally denotes. When a whole is used as the part or a part of a thing is put for the whole
"The world treated him badly."
The whole world did not treat him badly only a part. - The whole is used as the part
"Twenty sails came into the harbor."
Meaning twenty ships came into the harbor. - A part is used for the whole