Impossible to say definitely. The best thing to do is score some bone blanks from ebay or StewMac and test.
I depends upon a few things, not least the density, mass and hardness of your existing nut and saddle and the equivalent specs of the piece of bone you use for the replacements.
I've changed many nuts (and quite a few saddles on acoustic guitars and a few ukes) from plastic and Tusq to bone, from plastic to Tusq and from Tusq to bone. Sometimes it is hard to hear any significant difference at all. Sometimes the difference is obvious.
Where I notice a consistent difference is when replacing those cheap plastic nuts that are hollow underneath. Replace one of those with a good piece of hard bone and there is usually an obvious improvement to the definition of the sound.
If you file a bone nut blank and it feels gummy, or the file jams frequently then it's not a great sign. The blanks I have found to work best you can recognise as soon as you start to file. They are dry and brittle and the file doesn't clog, but files cleanly leaning dust instead of clumps.
Edit to add: If that "syn-bone" is the same stuff as I have on my Kala solid mahogany tenor nut, then I'm not very keen on it. When I next order a few bone blanks I'm definitely going to replace mine. That stuff seems too soft to me.