Is it scientific to attribute an event A, to cause B, where cause B was deliberate designed, with some sort of intelligent intent? Don't answer the questions beyond that
Well, the problem with not answering beyond that is that your example is completely rigged. There are several major fundamental problems here.  

First, you completely fail to mention the fact that the intelligence behind ID is quite literally not of this earth. Natural science might look at a honeycomb, see it is built by bees, and then find an odd looking fossilized honeycomb, and theorize that it was made by odd looking bees. That is fundamentally different than saying it was made by something not of this earth. ID has at its core the notion that something OUTSIDE the system we can observe is at cause here. This is not science in any sense of the word, it is mythology. When Paul Bunyan was having a wrestling match with babe his blue ox, they kicked up so much dirt they created the great lakes. No evidence of paul and his ox remain. i mean, really.  

Second, natural science takes an approach to knowledge that nothing is known scientific law unless it is irrefutable. Theories must have heavy supporting empirical data to back it up. ID turns this on its head and does an end run around knowledge and plays games with "probabilities". If no one can say how flagella on bacteria could have formed naturally, how in the hell can ID proponents come up with any sort of mathematically accurate PROBABILITY of flagella naturally forming on bacteria? If you don't understand it, you can't do statistics on it. ID jumps right over that hurdle and takes anything that doesn't have a complete, detailed, natural explanation and jams in their own statistics that say "well, it's so improbable for this to happen, that someone MUST have designed it". This is such a perversion of science. You can assign probabilities to something you don't understand. ID is just making up their numbers.  

Finally, your example has A->B, where B was deliberate design. that's all well and good for a rigged example, except that with respect to life on earth, "B" is unknown. Your A->B example might qualify as forensic science, if "A" were a dead body and "B" were a bullet in the heart. You see a bunch of dead bodies with bullets through the heart, the next time you see a body with a bullet through the  heart, you can probably figure that's what killed him. You don't have that with life on earth. You have ONE scenario, "A", and you have no other cases to observe or test. So, in that sense, A->B is not scientific if you've never actually observed "B". (btw, B is teh intelligent designer, which has NEVER been observed). So, in that sense, no, it isn't science.