I think you can do this by drawing your character to a render-target first (which includes alpha-channel), then apply any broken/bleeding effect to it. After that, use the render target as texture to draw it on the screen. Of course, another solution (which gives pretty the same result) is when your ship and its damaged image have the same size (in proportions), you can draw them both using multi-texturing.

Personally, I think using render-target is better idea, since multi-texturing is very hardware-dependent (or at least, more dependent, than the support for a single render target).