Yes, you could do the lasers in AE, or in PS if you render your ani as a seq. file(individual .bmps). If you have a "video paint" plug-in or program you can add laser beams that way. I did the beams in Bryce itself, just to see if I could, and I think it holds up pretty well. The only thing I added post rendering was the lens-flare glow when the ships are firing.
Realistic explosions can be problematic since the present version of Bryce doesn't have particles(maybe in Bryce 7?) but could be a doddle to add in post if you have AE and either "ParticleIllusion"(www.wondertouch.com), or AlamDV (http://fxhome.com) which give you the ability to composite great explosions, laser beams, lightsabers,etc.over your base "footage". Glad you found the ani interesting.:-)