If a star explodes while being sucked into a black hole will the explosion have any effect on the black hole?

Consider a binary system in which a star is slowly sucked into a black hole while the star continues to shed parts of its outer atmosphere, as stars do, and the black hole continues to suck in the material. Eventually, the star will run out of mass to sustain the hydrostatic equilibrium that keeps it together, which will cause our star to violently explode.

This serves as the plot of an incredibly good Stargate SG-1 episode, in which a wormhole is formed between a star and a black hole in an attempt to draw in the star's mass and blow it up, eliminating the system's fleet of hostile ships. But I'm getting off topic.

Where were we? Oh, right. The star is pushed apart by fusion, and it is pulled together by gravity. Insufficient mass combined with insufficient gravity results in a massive stellar explosion. The explosion's velocity through space is, I believe, at or below the speed of light.

Because the shell theorem states that all mass can be thought of as concentrated as a single point particle in the center, the Schwarzchild radius determines how far away the event horizon (the point of no return) will be from a black hole. A black hole is defined by its Schwarzchild radius, which is essentially the radius of a sphere that a certain amount of mass has to be packed into before the escape velocity from the surface of the sphere is greater than or equal to the speed of light. Say that in one breath.

Consequently, it is most likely that the star's remnants will first join the accretion disk orbiting the black hole and then be sucked past the event horizon. Since nothing, including information, comes back from beyond this horizon, we are unable to determine what exactly happens to the black hole's internal structure, but we do know that the only effect that comes from outside the event horizon is an increase in the black hole's mass and gravity, which in turn increases its Schwarzchild radius.

A star exploding while it is being drawn into a black hole would not affect the black hole itself because the black hole's enormous gravitational pull would be too great for the explosion to have any effect on it. Instead, the black hole would continue to absorb matter and grow in mass.