You shouldn't have any issues with bottle bombs, as you wouldnt' be using yeast to carbonate.
Root beer will keep a long time at 70 degrees.
The beergun is stainless, but the tubing for it, and any o-rings, should be dedicated to "root beer" only.
If you can force carb the soda, and bottle it cold with a much longer line at about 2psi, this might work very well. Otherwise, if it's warm or the serving line is the "regular" size, foaming will be an issue.