Sure it is possible. It is even common for senior people. I rarely have to ask others how something works because I understand the syntax, the database structure, the actual code, the business reasoning behind the code, and the limitations that people would have had in creating the code.
I believe that your boss is trying to make you more self-sufficient and to give you a better understanding that will make you a more valuable, senior employee. As such, he is clearly willing to allow the extra time it takes to figure things out for yourself. This may be a plus as he is grooming you for senior responsibilities or it may be a minus as he thinks you don't have enough actual knowledge and he wants you to gain it rather than always being dependent on others. Either way, it is worth your time to do as he asks. Additionally, he may have asked you to do this becasue the other person is tired of being bombarded with questions that you should be able to find the answers to on your own or he may be tied up on something critical that the boss doesn't want him pulled away from to hold your hand.
In any event, the boss wants it, so you really have little choice but to do as he asked. If I told you not to ask questions (which I probably only would do in the case above where the person getting the questions needed to be undisturbed for other reasons) and you did, then I would have a very negative impression of you as an employee.
Another point to consider is that often no one who worked on the previous code even works there any more. You have to gain the skill of figuring things out on your own. It is critical to your career development. Your boss is doing you a favor by forcing the issue.
Not only should you learn to figure these things out on your own, you should learn to retain the knowldge you get so that the next problem is easier to figure out. I find that inexperienced people are often in the habit of throwing away knowledge after to using it once and so are continually re-inventing the wheel. If you have more than a years worth of experience and you have to look up things more than 20% of the time, you are probably doing this.