Well, yes, it's 100% possible, but what part of a game engine are you interested in? The IDE? An interpreter? A compiler maybe? An IDE wouldn't be too difficult, just make a quick GUI system and make it save to a specific file format that you could then open in an external compiler/interpreter. As for a compiler/interpreter, a compiler to something like Java bytecode/Python bytecode is certainly do able, but not easy, while a compiler to machine code would likely be very difficult no matter who you are assuming you're not in a team. An interpreter in GM isn't a good idea since you're essentially magnifying performance issues. Even when GM is compiled, it doesn't compete with hand-typed C/C++ code (What things like the Lua/Python use for their interpreters).
Basically, I wouldn't try to make in interpreter in GM or an IDE either, but both are totally do able.