Like Nicol said, virtually every rendering system used in modern 3D games is a rasterizer. Your graphic card is also built with rasterization in mind, so if you implement a raytracer you either have to do it on the CPU or use some more recent "general computation on GPU" technologies such as CUDA because it's not supported directly by your hardware.
With that said, you "can" implement raytracing, rasterization, radiosity, etc., in virtually any rendering system - just don't expect it to run well.
For instance, I've written (for educational purposes) a rasterizer and a raytracer from scratch on Windows Forms and the only thing I needed from the library was GDI and the Bitmap class. Everything else was calculated by the application.
So the answer to the question "Is it possible to implement a ray tracing algorithm while using OpenGL?" would be: sure, but neither the software or the hardware will be helping you, and the result might not fast enough to be used in a game or another realtime application.
What most modern games do (including those built with the enignes you mentioned) is to fake some of the effects of raytracing and radiosity (i.e. global illumination) by using other techniques such as shadow mapping, depth of field and ambient occlusion, which can generate visually similar results with a much smaller computational cost.