Is an eps Illustrator file a full vector file?
If I convert a pdf file to an Illustrator eps file, will it be a full vector file that will resize appropriately?
The EPS format is merely a container. What is in that container can vary.
An EPS can include 100% raster data. An EPS can include 100% vector data. An EPS can include any combination of raster and vector. The simple fact that a file is saved to the EPS format does not mean it's automatically vector.
Unlike Photoshop, it is possible to create 100% vector eps files with Illustrator. However, much depends upon how any file is constructed within Illustrator. If you use the effects for shadows, or blurs, or glows, you are embedding raster data in the EPS.
So the reality is... An EPS from Illustrator can be totally vector, but it doesn't have to be.