It is possible, but it is a PITA. Windows uses a hard-coded font to hold the EMOJI. So you need to replace that specific font with one you edited. But the Windows EMOJI character format is "unique" and so you have to also have tools to generate that format in the updated font.
Why Microsoft has made this situation so difficult is a different question. This technique is documented in various web-discussions. Most commonly to grab old Win10 emoji to replace uglier Win11 emoji.
What they did make easy, since Vista, is to add your own PRIVATE emoji/glyphs in the custom code-point range of Unicode. But you'll likely find many "coding" fonts already take advantage of that code-point space.
Many applications that work with emojis use some kind of a browser-ui surface and in that case they can use any font they want to for emoji/glyph display within a browser (not desktop app) context.
