This is not a simple yes or no question. The answer is not as black and white as you think it is. Ask yourself what your life goal is and for how long are you staying in Germany. If you speak good English, you can do most of the things in Germany just fine. There are (of course) signs and information available in English in most of the places. As a tourist, you shall not have a problem. Nevertheless, when travelling, you have to plan your trip. Once, in München ,I was in a hurry to catch a train from the Hauptbahnhof to the Flughafen. I did not have much time left before my flight and could not find the platform from which my train was leaving. That happened, because I did not know that in München you have to go downstairs to get on certain platforms. I did not see a sign saying which direction my platform was. I decided to ask a worker at the railway station. I saw a man wearing a railway uniform and asked him if he spoke English. His answer was “No”. He wanted to turn back, when I said in German: ‘Ein Zug nach Flughafen?’. He perfectly understood my imperfect German and replied in German that I should go to the right, then downstairs. He also told me the numbers of the trains that went to the airport. The information was very helpful. I rushed downstairs and caught my train just before it left the railway station. I saved the time, which allowed me to be at the airport just in time.If I did not speak any German at all, I would have troubles to find an English speaker to show me the direction. Speaking and understanding German is helpful when you travel across the country.
If you are staying in Germany for a short period and being occupied with lots of work, that does not include German language, you shall not be worried about not learning German. If you find out about the train, bus schedules etc. in advance and will not be in a situation you do not know the direction, you shall survive there speaking English just fine. However, if you plan to stay in Germany for a longer period (studying or working), it is advisable to study German in order to have a comfortable life. Believe me, this is not fun, when a person on a street asks you a question and you have no idea what the question is about. In addition, sometimes, when you go by train, the announcements are in German only. Maybe they are not major announcements, but to be on the safe side, it is better to understand them. Some shop assistants and waiters might not speak English that well either.
It is important to understand signs written in German. One day I misinterpreted a sign in a supermarket saying (in German) something like ‘at the checkout counter number 4 you may only pay in cash’. I saw people moving to another checkout station and I thought that number 4 meant the number of items you could pay for at that checkout counter. Later (of course!) I realized that number 4 was too little to be the number of the items. It wasted my time standing in the longer line, because of not reading and translation the sign carefully.
Another day I broke the rule when throwing old clothes into a special container. Only after I closed the lid I saw a sign Wir sammeln in Tüten verpackte… Of course, I took my old clothes out of the plastic bag before throwing them away. hehe
A friend of mine got into a funnier situation. He went for a job interview shortly after he arrived in Germany. He parked his car to change the clothes. He was going to get out of the car when the police came. They wanted to arrest him, because he parked the car in a parking lot that belonged to the property of the police (to be precise, the favorite parking space of the Police Chief of that city). Sadly, the physical appearance of a friend of mine (dark skin and hair) was not in his favor either. This story has a happy ending, though.
As an expatriate, of course, you shall learn the language. In my view, speaking the language plays an important role in how well you adjust to a new life. Understanding people around you, will save you from possible troubles and will help you to feel more like a part of a new society you live in.