Would the same bezier curves be used in font rendering? And do we have GPU bezier drawing functions or shader kernels available?

Yes, TrueType fonts use quadratic beziers while PostScript/OpenType use cubic beziers, and modern GPUs offer acceleration through tessellation shaders and compute pipelines like NV_path_rendering extension.

Note that while cubic bezier curves are nice for designing shapes, quadratic bezier curves allow a much more optimized renderer. It's usually worth approximating.