Given this directory tree:
src/MyLibrary/MyHeader.h
src/file.cpp
file.cpp:
#include \"mylibrary/myheader.h\"
...
Compiling file.cpp works
The case sensitivity depends on the Operating System. Windows is not case sensitive. Linux is.
EDIT:
Actually, as observed by Martin York's comment, the case sensitivity depends on the file system. By default Windows uses a case insensitive file system, while Linux uses a case sensitive one. For whoever is interested to know which file systems are case sensitive and which aren't, there is a comprehensive list on Wikipedia: Comparison of file name limitations.