I wish to build a compiler (GCC port) for Linux, so that the built GCC runs on Windows and creates executables for an embedded platform.
Is the above possible?
Yes, it is possible.
It also utterly painful to try to do this yourself -- it is OK on Linux, mostly, but very tricky on Windows. My suggestion is to see if some ready-built compiler from a place like DENX.de, CodeSourcery, or the manufacturer of your embedded platform is available.
I have become a huge fan of the CodeSourcery compilers for platforms like MIPS and Power Architecture. They tend to come with variants for big- and little-endian, various Libc flavors, and to have both bare-metal and linux-target versions available. See their pages about their Lite edition
Building your own cross-compiler and toolset is a right pain.
If your target is running Linux, I suggest doing your cross-work on a Linux box as well, saving you plenty of pain. I use VmWare for that express purpose. You cannot expect to build a Linux for a target on Windows, for example.