Can make a difference. It depends upon a few things, not least the quality of the bone. A good, dense piece of bone can make an instrument a little brighter than a cheap plastic saddle. You may also find that wound strings wear little grooves in plastic saddles - good, hard bone is more resistant to this.
If your uke is very bright, you may want to consider another option - ebony, perhaps - or stick with the plastic.
The difference in sound is usually marginal - sometimes not easily heard at all. The greatest difference is usually when both nut and saddle are swapped out for bone.
Some bone blanks are poor quality. These often feel kind of gummy when you try to saw, cut or file them. What you want is nice dense hard bone that rings when you drop it on a hard surface.
The great thing about tweaks like this is that the new parts are cheap, and if you keep the old parts safe then the job is reversible if it doesn't work out.
If I were you I'd try it and see. What have you to lose?