No. The Van Allen Belts are not some kind of 'force field' or barrier like the kind you find in science fiction programs. They are, in stead, regions of space around the Earth, roughly resembling two nested donuts around the magnetic equator of the Earth. They contain trapped, high-energy electrons and protons at a flux of several million particles per square centimeter per second. In other words ,a 1 square centimeter surface will get about 1 million of these particles flowing past it each second.
Yes they are very deadly regions to pass through if you are only wearing a spacesuit, but the Shuttle and International Space Station orbit well below the innermost edge of these belts. The Apollo astronauts who went to the Moon did pass through these regions, but the passage only took about a half hour, and the accumulated dosage they received from inside the Command Module was something less than 1 rem, or the equivalent of a few dozen chest X-rays.