Not directly. On the COSMAC VIP, the framebuffer was located within addressable memory. This isn't the case with modern interpreters.
More generally, a CHIP-8 program can examine its own frame buffer by drawing a pixel at a time to the screen and checking vF afterwards to determine whether a pixel was toggled.
If your goal is automated testing and you're familiar with JS, you could probably hack up something using Octo's compiler and emulator in a "headless" fashion; they shouldn't have any direct dependencies on browser APIs.