If I create a C++03-compatible header, and use the same compiler (g++), will this work?
In general, yes. Once a module is compiled, the interface tends to be the most important part.
There may be ABI issues, though, depending on whether name mangling or anything like that changed. If you can use it as a shared library, there's a decent chance you can use it statically as well.
More important, however, is standard library versions. Those very likely changed, so passing std objects between the two should be avoided at all costs.