BRS has a vid on their website about using their reactors, they give you a recommended formula for mixing gfo and carbon. Gfo will fuse together and lessen the efficiency by limiting the surface area, that's the main reason to tumble the gfo. But yes you can mix them, mixing gfo with carbon will separate the gfo so it won't fuse together, go check it out. There are some drawbacks as gfo tends to last longer than carbon, but if you are only running one reactor, it's a good option.
It may also be harder to dial in the GFO because you will need to adjust flow and amount of GFO to get the correct PO4 levels in your tank. Especially when first setting it up.
You'll also likely throw away a lot of good GFO when changing out your carbon.
By the way, make sure you are testing Nitrate and Phosphate regularly when running GFO and Carbon. If you bottom out PO4 or Nitrate, it will wreak havoc on your tanks stability.
I run both at a 1-3 ratio, 1 part GFO and 3 parts rox and it works fine.
The carbon will exhaust sooner than the HP GFO so I have found this to be a good ratio.
I do not run this 24/7, only when I see an increase in the nutrients.