No, and like you, I wish this was possible, though my reason is aesthetic and I don't think yours is.
Unfortunately, vscode extensions require a browser-like environment to run in, so the front-end must run in a graphical environment of some kind. You could render vscode in a browser, capture that, convert it to text, then send that text to a remote terminal at 30-60 FPS. There is a text-mode browser which does exactly this using headless Firefox in the background, and that could be used, perhaps: https://github.com/browsh-org/browsh, but it does everything on localhost, not remotely. At best this would be a hack that required a LOT of bandwidth, and at worst it would be unusable.
What I think you want, though, is probably just what the normal vscode "Remote" extensions provide. You can run vscode remotely via SSH and connect that remote backend to a locally hosted frontend which has nice, low response times.