I'm here to save you the bother. It's an unqualified NO!!!
So the problem with sassafrass is that pesky cancer-linked drug-precursor compound safrole. Sure there are methods to extract the safrole but the ones I could find were all about the safrole. The root itself was treated pretty roughly and probably wouldn't be suitable for soda-making. Many of the root beer extracts are safrole-free, but I suspect that many are also sassafrass-free. I wanted the real deal for my soda.
Imagine my surprise when I find out that there's a part of the sassafrass plant that is available that naturally doesn't contain any safrole. It's the leaves! Sure, it's probably not as potent as the root, but surely this can be compensated for simply by using more of it. It's known as gumbo fil'e (file with a fancy e). I found a supplier that had an unadulterated, pure leaf power. I just had to try it.
I fired up my usual root beer recipe (scaled to 1/2 gallon) and up the sassafrass from .125 oz (root) to .17 oz (leaf) (roughly 40%). Half-way through the simmer, I say to myself "that smells a bit off and has an odd green tint to it. Better throw in some sarsparilla." The sarsparilla improved the color and aroma dramatically. Let it sit, cooled it down, force carb'd in a soda siphon.
The resulting beverage smells off, had an odd, green tint to it, and the mouthfeel is just awful. It's gummy and chewy in ways that soda should not be. If you're familiar with cider-making faults, it reminded me of rope. I couldn't even bring myself to swallow that first swig. Straight down the drain it went. A complete waste of time. Hopefully someone here gets a kick out of the tale and it saves someone else from the same fate.