I'm a Sephardi Jew with no previous connection to Judaism, can I join it nonetheless?

I'm not sure where you would fall in each sect, but I do know that genuine conversions are accepted in most denominations. I have no genealogical Jewish heritage (...mostly, maybe? I really don't know for sure) but completing the conversion process will make me a Jew - a complete Jew, culturally and religiously. I don't see why it wouldn't be the same for you.