I don't know about synthetic. I use cheap store-brand mineral-based oil.
Still, go ahead and try it. I guess my point is, try a range of different oils and see what works. That's how I ended up with my selection, but it may vary with bushing wear, aftermarket tubes with different drillings and/or clogged holes. Aside from viscosity, any oil should work. I think that due to the lack of any valving in these forks, the anti-frothing agents in fork oil aren't really going to matter much...