As a visual learner myself, I can see why this would seem appealing, but having tried it myself, I have to echo Some Dude's sentiment that you really don't need this. It might be neat to play with a few times, just to see what kind of fluctuation exists in your voice, but overall, its very unlikely to help you become a better singer.
The reason is that if you're concentrating on finely controlling your voice to a microtonal degree, to make a small, jumpy bar fall into the right location, you'll completely miss the wonderful sensation of hearing a unison between you and a reference pitch, which is what you should be aiming for. You'll also be using your voice in a way that's atypical for singers, and which will contribute little-or-nothing to your future pitch control, when singing without a tuner. Not to mention the fact that, in many singing styles, perfect 12-TET pitch isn't even a necessarily desired quality anyway.
Nevertheless, as Karen mentions, a free tuner app on your smart phone can show you this in (almost) real-time. As an example, on my Android phone, I use DaTuner Lite.
But typically you'll want to practice with some sort of instrument to give yourself an audible reference pitch, and learn to match it. The upshot of being a visual learner, though, is that once you get a feel for scales and matching pitches, you should be able to easily pick up sight singing, which is a far more appropriate application of visual senses to music.