In most cases, yes — partially. A driveway that has had a stone surface for years has typically developed at least some compacted base material that contributes to the new foundation. The contractor evaluates depth, drainage, and stone quality, then supplements with additional processed stone as needed.
When the existing gravel is too thin, too contaminated with soil, or sitting on a soft subgrade, more excavation and fresh base material are needed. This is the biggest variable in cost between conversions — a conversion where 80% of the base is already in place costs less than one where the whole foundation needs rebuilding.