Yes, you can transfer your Site Audit Pro database to storage on your device.
Go to Settings > General > Import/Export Database - then choose to "Export Database". This will move a copy of your database to the location shown beneath. You will now need to access that location either on your computer using an Android File Browser, or move over the storage card if one is in use and it can be used on your computer or a second device. If you're using a computer, you will need to save these files at an easy to access location.
If you're transferring your files to a second device, install Site Audit Pro and then access the Import/Export options again. Make a note of the location displayed for this device and then use your computer to access this device's files using your File Browser. Go to the location given and save your files there. Once this is done, you can tap "Import Database".