Given what assumptions?
If you're going to postulate an Artificial Intelligence that can do anything a human being can do, then presumably by definition the answer is yes. So I'm going to assume you mean with current technology or something reasonably close to it.
Next question: In what sense?
In the simplest sense, it would certainly be possible to store the law on a computer and make it easily searchable, have cross-links between related laws, etc. I'm really surprised that more hasn't been done in that regard. The technology exists to store the text of the law on a computer in HTML, create abundant links, provide text searches, etc.
The first place where it gets tough is when you say things like, the computer will tell you when a proposed new law conflicts with an existing law.
Some cases would be easy. If someone proposes a law reading, "The speed limit on interstate highways shall be 85 miles per hour", I could imagine a computer being able to find that there is an existing law that says, "The speed limit on interstate highways shall be 80 miles per hour".
But what happens if you say the same thing in different words? Like what if someone proposes a new law reading, "No one shall be allowed to drive a car more than 85 miles per hour on roads making up the interstate highway system." Now the computer has to figure out that "interstate highways" and "the interstate highway system" are the same thing. That may seem obvious, but just because two phrases share common words doesn't make them the same thing. How would it now that those two are the same but, for example, "the Marines" and "the merchant marine" are very different? How would it know that a "speed limit" refers to the top speed you can drive a "car" and not, say, a boat, or oil through a pipeline? How would it know that "speed" here means "velocity" but in another law refers to a drug that acts as a stimulant? Etc.
What happens when a law entered into the computer is ambiguous? Like in my example above, does this speed limit apply to trucks and motorcycles?
Many laws are very subjective. For example, to successfully sue someone for negligence, you have to show that he did not take the precautions that a "reasonably prudent man" would take. Who is to say what a "reasonably prudent man" would do? That's full of subjective evaluations.
Similarly, I'm somewhat active on a forum for writers, and a question that routinely comes up is, Copyright law says that I can copy short quotes from another person's work without permission. What is "short"? Can I copy 50 words? 100? 1000? There is no hard number. The law further says that factors for the court to consider when deciding if such copying is "fair use" are whether it was copied for educational or research versus commercial purposes, the nature of the work, etc. What makes something "educational"? What about "the nature of the work"? Etc.
Laws do this very deliberately because there is the constant struggle between the letter of the law and the spirit of the law. Someone else mentioned that the law forbids breaking into someone else's house -- but no one's going to prosecute you if you did it because the house was on fire and people were screaming for help. It's against the law to take someone else's property without their permission. But if a maniac is holding people hostage, and in a moment of carelessness he puts down his gun and looks the other way and one of the hostages grabs the gun, I really doubt the hostage would be prosecuted for stealing. Etc.
Perhaps you wouldn't simply type English text into the system, but would have to describe laws using a carefully-defined language that eliminates a lot of these complexities and ambiguities, a language designed to describe laws in a way that a computer can process and analyze. But would it be possible to create such a language? To say, "Yes, the computer can solve this problem. We just have to invent a language to describe the problem in a way that the computer can solve" is to talk in circles. Like, "Yes, I can prove that it is possible to build a spaceship that travels faster than light. You just have to grant me the one tiny assumption that someone else will provide me with the plans for a faster-than-light engine."
So in conclusion: I'm quite confidant that it could be done in a limited way. But to meet all the conditions you describe? That would require advances in AI far beyond what anyone has accomplished to date.