Upvote:9
If you are currently seeking asylum, the answer is no. You must stay in Italy and complete the procedure. At the border to Germany, the police would stop you. If they determine your identity with your biometric data, they'd send you back to Italy.
Once you have been granted asylum, you should get a Schengen residence permit and also a 1951 Convention travel document. With those you can travel, see this answer.