Yes, and no.
If you place an order or save your progress when designing - these images will be available for reordering purposes or to help you complete the saved project.
Sadly, these uploads won't automatically be available for other projects or products. We do however store recently added images from the current design session, which means you won't have to upload the images multiple times.
These images are cached and available in the "Recently added" section at the bottom of the upload interface.