Yes. That is what wildcard certs are for, and they're not new. They're pretty expensive though, when they come from trusted root CAs. The cost benefit is only there if the wildcard cert saves you money vs. getting individual certs for each unique DNS name in question. So, it's a simple issue of doing the math.
Do they work with OS X Server?
Yes. It's just a cert. And any cert can be used with any web site; it's the client (browser) that decides about things like host/cert mismatches, etc., and a wildcard cert for *.foo.com works for [anything].foo.com.
How do you install it? The same cert on every server in question?
Yes.
Anyone done this?
Yes. ;-)