The short answer is NO , other apps cannot access your Photo Vault. Any content you add to your vault is encrypted and only viewable from within Keepsafe. You can read more about How Keepsafe protects my data here. It is, however, possible to send files from other apps into your Photo Vault. For example, you can send a selection of photos from your system provided photo app into your vault. Once inside, they will be encrypted and no longer visible to apps outside Keepsafe. It is then safe to delete the originals from your system provided photo app.
While other apps cannot see what is in your vault, Keepsafe can send content from your vault to other apps if you explicitly ask it to. For example, you can add a photo to a text message or send it to your email app as an attachment. These actions will not remove the files from your vault, and effectively provide an unencrypted copy to the selected destination app.
If you do want to remove files from your vault, make a selection, tap the share button, and choose the export option. Exporting will decrypt your files to their original state and move them out of Keepsafe. You can read more about exporting photos here.