Sounds like your OS will be on the SSD, right? SnapRAID won't affect or use that at all. With 3x4TB, you will have roughly 8TB of storage since the 3rd HDD will be used for parity. There's no reason you shouldn't be able to "fill them to the brim".
I think you are confusing what happens when you mix drive sizes. You will always be limited by the size of the Parity Drive. If you have a 2TB Parity Drive and a 3TB Data Drive, you will only be able to use 2TB on the Data Drive. As long as the Parity Drive is as big as the largest Data Drive you can use all of the space.