There exists an open-source engine designed for Dreamcast that operates on OpenGL 2.
https://github.com/cjcliffe/CubicVR
Since Godot supports GLES2, it may be possible to write a GLES2 library for that console and get the engine running with very minimal tweaking.
I'm no expert on low-level programming myself so this is only a mildly educated guess, but for now I'm going to wager that it is in fact, possible to make Godot Engine work on Dreamcast. It's just a matter of when someone makes it happen.