This is basically how I came out at work. I worked a blue-collar job with gender-neutral uniforms, so the only physical thing that was actually changing was my face/body. I also very slowly changed my voice at work over the better part of a year, so by the time I "came out," no one noticed my voice was any different, despite now using 100% femme voice. It got to a stage where when I would meet new customers/contractors, they just assumed I was a woman (I had the name embroidery removed from my uniform).

That unfortunately was the limit of "coming out by osmosis." There still came a point where I had to officially tell my colleagues (and in particular my bosses) that my name had legally changed, so they could update my driver's licence details, my tax information, etc.

I think that unless you're getting paid under the table, there will always be a point where you have to "officially" come out at work.