Yes. You can record from all inputs at the same time to individual tracks to any DAW.
Ensure that you are setting up Pro Tools correctly. You may need to contact Avid for further assistance.
This Sound on Sound article is fairly comprehensive as well.
You should also ensure that you have the AR12 properly installed and updated with Universal Control.
You can also test your AR12 using Studio One 2 Artist to ensure that your AR12 is installed and working properly.