I started singing in the privacy of my studio, quite young; so I guess it took a while, but nothing excessive.
I'm not privy to your use of your accordion. If you market yourself and play out, I would think it is definitely worth it. There are many more opportunities for someone who sings and plays that for someone who only plays. Even if you're just playing for yourself and your family, being able to sing adds more to your playing.
One caveat: make sure you can carry a tune or it can get pretty dicey !