I don't think so...
I do know for a fact that the earlier harps were just fiberglass props where the "strings" were real colored string looped around pegs at the neck-- and you can see that really pretty clearly if you look closely at some of the pictures.
But as to the material of the neck, it looks like the entire body and neck is some solid wood and there is some kind of brown leather or something similar over the neck to make it look like routed wood. In a picture where Uhura is holding the harp, it is much clearer how the leather or whatever is slightly peeled away from the body near the "butt-shapped" curves that are toward the top.
But one should also probably note that there are at least three different versions of the harp seen in the available pictures, each fairly different from each other in size, shape, and composition-- so there are no hard and fast rules. Harp creator, Wah Chang, made different versions; one even for his wife.
In the Trek Tech manual it is said that of all the 300 or so Vulcan lyrettes made, or surviving, the most "famous" ones had been made by three different luthiers. So that can explain a lot for people who wanna say that a certain version doesn't look authentic, heh heh.