I don't know of anyone who has done a PhD in this, but I do know someone who wrote a book on public art in the North West of England, if you PM me I can send you the details. I think your project sounds fine, interdiscplinary is all the rage, in the arts anyway. I'm interdisciplinary: art history and film - and studies of national identity (not sure if that last one merits another multiple disciplinary browny point, I guess its a bit of anthropology - Benedict Anderson's ideas comes into it quite a bit).
My interdisiplinariness has meant more reading etc - you have to get to the bottom of two distinct areas, but it's exciting to build something new out of that, and it will mean your work is more original - it sounds like your project has a lot ot offer, I'm presuming you're looking into art in public society. Also, I'm sure this kind of research has been done quite a lot before, maybe it's an established sub-discipline; art galleries and arts organisations are always very interested in this kind of thing.
.