The Parkinson's Voice project has now had over 5,000 replies.
A paper by Tsanas et al.  gives more details. For instance, with their system "UPDRS can be estimated to within about 3.5 points difference from the clinicians’ assessment, which is clinically useful given that the inter-rater variability for UPDRS can be as high as 4-5 UPDRS points."
I think, however, it will be better than what that implies. This is because what we really need is a measure of the severity of our Parkinson's, per se, not an estimate of our UPDRS score. My hunch is that the quality of one's voice reflects deeper, more visceral processes better.
 "Using the cellular mobile telephone network to remotely monitor Parkinson's disease symptom severity"
Athanasios Tsanas*, Max A. Little, Patrick E. McSharry, Senior Member, IEEE, Lorraine O.Ramig