I personally have always had a small Adam's apple, since before treatment, and let me tell you, a female with a small bump is a lot more noticeable than a male without one. I honestly don't even notice that type of thing on people unless it really protrudes. I'm guessing it has to do with genetics and sometimes weight, whether or not you develop one.
But I can't sit here and tell someone not to be self-conscious about something on their body, so if you really do feel it's something you need for transition, then look into an implant. Although I wouldn't suggest doing so until you've been on T for a few years/have seen how you turn out.
I don't think it's a common surgery for trans men simply because it isn't a necessary part of transition. Most people I know would never question if their noticed a man didn't have an Adam's apple. It's just a man without one. It happens. More people are going to look for signs of facial hair than anything else.
I personally get grossed out by really big ones, I don't know why. Used to have a kid sit next to me in class who looked like he had an actual apple stuck in his throat, and it would freak me out. I don't even like touching my own. But hey, whatever makes you happy. It's your body, you do what you feel you need to to feel comfortable in it.