I think that depends on what you mean by “support.” If there’s a problem with the proprietary implementation, I would hardly expect Stan developers to be able to do anything more than recognize that there is a problem with that implementation and point users to the support staff for the cluster. However, you’ll have to expect that users of Stan on those clusters will almost certainly be using a proprietary implementation.
I’ve noticed that on a cluster, there’s usually a “canonical” MPI implementation provided by the cluster’s vendor. For SGI clusters, that’s SGI MPT, and for Crays, that’s Cray MPI. Whether there’s an alternative to that implementation depends upon the cluster. On SGI clusters, I’ve noticed that there is usually at least one alternative implementation which works at least as well as MPT. However, on those clusters, that implementation is often Intel MPI, which is also proprietary. On Crays, using anything but the default MPI implementation is dicier. There is a so-called “cluster compatibility mode” that allows for alternative MPI implementations to be used, but in my experience, it is both cranky and slow.
In my experience, I’ve also found that support staff of clusters either highly discourage or outright forbid users from using an MPI implementation that isn’t already installed on the cluster.
FWIW, my experience is with clusters provided by some sort of supercomputing center that provides remote access to its clusters.
I suggest that you might want to look at what other open-source projects that use MPI already do. You may also be able to get some degree of informal help from those who already use a cluster, though of course that depends on how busy they are, whether they’re working on something that would exercise Stan’s MPI capabilities, etc.
It really depends. However, so far, the proprietary implementations I’ve seen do support GCC.