I wouldn't count on this ever happening, at least not for years. Since FPSC:R is still based on DirectX rather than OpenGL, the path to get it from desktop to browser is much more complex than porting an OpenGL app to WebGL, for instance. There have been some DirectX-capable browser plugins built for specialized engines (i.e., WebVision) but it would still be a monster undertaking to optimize and implement such a plugin for FPSC:R. The desktop version itself still struggles with performance so getting a good experience within a browser is unlikely.
TGC did have some success a couple years ago porting AGK-based apps to WebGL for playing in a browser with Freedom Engine, including some FPS maps. However, that project was abandoned and has no correlation to the current development track of FPSC:R.
PC SPECS: Windows 7 Professional 64-bit, AMD Phenom X6 1100T 3.60 GHz CPU (Passmark: 5934), NVIDIA Geforce GTX-680 2GB GPU (Passmark: 5712), G.SKILL 16GB DDR3 1600 (PC3 12800) RAM