Is it possible to use the Boost.DateTime library from C, and if so are there any examples available (preferably covering the build process using gcc-type tools)? I've searched the Boost documentation and the internet in general, and it seems theoretically possible, but have not found any clear answer one way or the other.
No. Boost is a C++ library and Boost.DateTime is no exception. If you look at any of the DateTime headers you'll see C++ features everywhere, from classes to templates to namespaces and much more - none of which are supported in C.
You can, however, create a wrapper library in C++ which exposes the functionality you need as pure C functions, then call those from C.