You need to go through most of it i'd say.
Learning a language isn't a simple task. For Japanese you need all three parts, Hiragana, Katakana, and Kanji to read, speak, and write fluently.
Fluency, In my opinion doesn't come from learning, it comes from experience and practice.
Being involved with Japanese natives and Japanese speakers (and Japanese anything in that matter) is the key to becoming fluent as you will be listening and speaking to them as well as many other things; Learning Japanese will help you do this, fluency comes from doing this.
The lessons on this site go as far as, I'd say, half of a semester of beginning Japanese in college. Would I consider that fluency? Probably not, unfortunately. But I think this site is really wonderful for the pace that it introduces the writing system, verb conjugations, and simple grammar patterns. It's great to have motivation throught the language learning community and fun drills, isn't it? Once you finish all of the exercises in this website, you will have a very strong base from which you can use other sources to expand your Japanese proficiency, and like others have said, with more experience with reading, speaking, and writing, you will become fluent!
Learning online or through textbooks is a little problematic, because although you can achieve a high reading/writing level, becoming conversational is a whole other realm! Watch Japanese TV shows and movies and listen for vocabulary words that you recognize. Have any Japanese friends? Meet up with someone on a regular basis IRL or over Skype and do a language exchange. (Talk to me!)