There's no such thing as an "unknown" band. If you're a band, and you play out, then someone must know you. I've played gigs where it was us and the bartender and two drunk people who left after awhile. So those three people, outnumbered by the band, who probably don't care one way or another, "know" us as a band.
"Unknown" is like "organic", it has a meaning beyond it's formal definition. I think that meaning is "not famous", and by "famous", I mean most people in the world know who you are, or can google you and see how many people think you are peachy-keen. So I ask, "How well known do you need to be?". What do you want out of "fame"?. You can be a local hero and that might be enough. If you want more than that, maybe you need more fame.
I have written before about the challenge of exciting an audience. You can do this in your home town without any help from the rest of the world. If your goal is to see if it works in other towns, or your town is small and you need more places to play, then you might need more fame. Maybe you want to earn some money, or... (dare I say it) a living. Well, then you definitely need more fame, because, as the composer Georges Bizet (Carmen) said, "What a beautiful art, but what a wretched profession".
To expand your territory, you need to play better and work harder at the business of music. The more you expand, the harder you must work. Can you do it? Is it worth it? How much is enough? Can you be satisfied?
A friend recently told me about two musicians, one motivated by ego, and one by creative passion. I think both are valid reasons to pursue fame. In fact, the steps you need to take are almost the same. Given equal resources, I imagine ego-driven musicians have a better chance because they aren't limited by their creative needs. They can change what they're doing to advance their quest, whereas the path for those with a specific creative vision is narrower.
So, can an "unknown" musician find fulfillment? If that musician is you, then you should be honest with yourself and consider what you want against the possibility of getting it. If you want to play fun gigs and meet people, and enjoy music, you can have success anywhere. But if your goal is world domination, you better get started, 'cause time is running out.