Yes, you should be able to.
The contents of the platform SDK headers RAR file should be good for compiling most windows applications, as well as programs that depend only on the standard C/C++ libraries.
If the windows applications use MFC or ATL you might be out of luck (the free version does not have headers or libraries for MFC or ATL as far as I know). If you need DirectX support it might be necessary to download additional libraries or headers from Microsoft (they are all freely available, I think, from MS'es web site).
Bottom line is: As long as you set up the compiler, IDE, and all headers / libs properly, you should be able to compile most programs that depend on the Windows API on its own.