Does code written in microsoft visual c++ using windows API will work in Qt?
If not is their any way to convert that code to Qt supported language?
Qt is an API, like the Windows Platform API, both beeing used with the language C++. You might use code using the Windows Platform API within your Qt projects.
Qt itself uses lots of Windows platform API internally (on windows, obviously, not on Linux). Are you looking for automatic code translation between code written for windows using native APIs to Qt APIs? If so: don't hold you breath. I do not think there is or will ever be a reliable way to do that.
P.S. Moving. This has nothing to do with language bindings.