Er... Your question as stated is based on an incorrect premise.
All headers in VS compiler are required to be included. There's no way around it.
Precompiled headers feature does not affect this general principle it any way. The only difference is that in projects that plan to use precompiled headers the headers are normally included indirectly, through a special intermediate header file. Nevertheless, you can't just forget to include some header file, regardless of whether the project is using precompiled headers or not. All headers must be included in all cases, directly or indirectly.
A project that's using precompiled headers will compile perfectly fine on any compiler that knows nothing about any precompiled headers at all.
So, the situation you describe simply cannot happen in practice. If it does, they you must be leaving out some important detail about the problem.