Would a basketball explode when filled with helium

The helium is lighter than air so the ball will have slightly more uplift for its weight so it would feel like it was in less gravity - so it would bounce higher (if you throw it at the ground at the same speed rather than drop it from a height). This would be a small effect probably changing the weight of the ball by about 22g.

The other effect is that helium is a better approximation to an ideal gas (lots of point particles bouncing around) than air. Air tends to loose more energy to making the particles spin and vibrate etc than helium does so it looses energy when you compress it and expand it. This means it is less elastic so the ball will have more energy after the bounce than it would do with air. - this is why expensive tyres are often filled with a noble gas like neon or krypton to reduce fuel consumption.