The answer to the question is yes you can be self-taught Japanese as I am albeit well and truly out of practice a number of years now. However, what matters is just how far you want to advance your studies; fine learning the basics from a text book which of course you will need as you will the hiragana and katakana script. As for fluency then that is a different ball-game, the problem being people don't talk like text-books. I notice when listening that Japanese not infrequently miss out verbs and of course use a few colloquialisms and expressions with which a foreigner may or not be familiar - no big surprise there.
For example the verb iru after the -te form of the word and the suru verb often gets missed out giving the impression, as far as I can deduce that a sentence has been left hanging in mid-air (people please correct me if I am wrong).
In addition the whole way of saying some things are so different that a foreigner would never ever think of saying it, here's and example from the Japanese drama 'One Liter of Tears;' Aya, the central character at one point says: 'when I put my hand to my heart I can hear it beating' (mune ni otte miru doki doki oto ga suru. The
literal translation of what she says is; 'chest at it place hand when put thump-thump sound does' (well something like that)
How would you know that? The simple answer you wouldn't so you would have to do hell of a lot of listening but it's not impossible as I had a friend who spoke reasonably fluent Japanese without ever having lived in Japan which he achieved by mixing with Japanese people.. Just how 'fluent' he was I don't know - sorry to say I fell out with him rather badly so I guess I will never know.
Items of use: Microsoft word has a scratch pad on the language bar when typing in Japanese where you can draw a character select it to print and then you can copy paste it into an on-line dictionary (I use tangorin) where you can also build up a vocabulary list.
The comedy 'Attention Please' is available with subtitles in Japanese script and have used Word the way described above in conjunction - real hard work but for some maybe the only way. Beware the DVD series is horrendously expensive as so many materials you may use for more advanced and worthwhile Japanese learning are!
Do build up your vocabulary, although mine is only around 1500 words at present I find can recognize a good many words. The book I found most useful for vocabulary is 'Japanese but not so much for grammar is 'Japanese for Today' although it is only available second having priced itself off the market.
Much will depend on just how determined you are or if you can logically find the time as there is no doubt the demand of learning are greater than European languages where resources are more abundant and cheaper (I am assuming you live in Europe). Good luck and I hope you find my post of use.
Ps: To the OP: you may already realize good deal of what I have said since you have learned German and will no doubt know people don't speak like textbooks but in Japanese the difference is more profound, in addition I am considering those new to learning Japanese who may not have done any foreign language learning.