I would plant them in the fall, about the time the winter rains start. They will be ready to grow when the weather warms. Al

The answer to the question in your title is yes, but with a lot of complexities (at least if you ask how much roots grow when the tree is dormant). I don't think you are looking for a lot of complexities, but here are a few generalized approximations:

1. All tree roots grow to some degree when the ground in which they are growing (at root level) is not frozen.
1a. In your area, roots are able to grow throughout the dormant season, if planted in-ground.
2. Growth rate, during dormancy is both species and environmental dependent.
3. Most species' roots grow significantly during dormancy.
3a. Ginkgo biloba general has significant dormant-season root growth.
4. Root growth is often greatly increased when the root-to-shoot ration is lowered (B&B trees, root-pruned trees, etc).

So what does this mean for your tree? It means that you should definitely plant them as soon as they are fully dormant. In your area, there are few woody plants that won't benefit from being planted in fall (Some species with fleshy roots, like pawpaws and some magnolias, are the exceptions). Planting in fall (or even winter, in your area) will allow the root system to begin to become established before the tree has to face the stressful time of the hot summer months. Below is a link to a guide that you may find useful.

Here is a link that might be useful: Planting a Tree or Shrub