No, but you can get fluent with 12+ hours a day.
In Mass immersion I said that if you study 18 hours a day, it will take you 1.5 years to basic fluency. Progress takes commitment. With one hour a day it might take you 15 years.
Think about it seriously and ask yourself the following question. Even if you somehow magically got fluent today, would you really need it if you were going to spend just one hour a day doing Japanese? What do you need Japanese for? Why do you want to know Japanese? Maybe Japanese isn't exactly what you want to do, and you need to consider something else.
And once you reach fluency, you want to maintain it. You don't want to forget the language. To maintain a high level of proficiency, you have to spend more than 1 hour on Japanese each day anyway. So even if you magically got fluent, it wouldn't last long.
In the very beginning it is easier to improve. Until a certain point studying Japanese for one hour a day is going to be sufficient. But it gets harder as you approach higher stages. Unless you up your immersion later in the process, before reaching a lower intermediate level you're going to reach a plateau, where you will be stuck.
If a low intermediate level is enough for you then it would be okay to go for it. However, this is not the level where immersion becomes enjoyable. So if you want to know Japanese and reach the highest levels of fluency where you can express yourself comfortably and effortlessly, what should you do? If you don't have time now, you could consider doing 1 hour a day for a while, but as soon as you can you've got to switch to the mass immersion mode and start doing All Japanese All The Time.