This is more going off the comment about science vs. magic, but there's a difference between Real World science and fictional science. While alchemy may be powered by a real concept, it doesn't exist in reality, so it's not just the movement of the tectonic plates that makes alchemy work. While that's the in-universe explanation, the out-of-universe (between-universe?) reason is that the Words are what makes it work.

That said, I'd say that alchemy would possibly function in badfic, especially ones that have a tenuous grasp of their own continuum's mechanics. Basically, the badfic weakens the solidity of the Words by creating contradictory elements, and the agents can bend it further to cheat a bit. It's frowned upon, because they're making a bad thing worse, but in a sticky situation it might be the only way out.

To use a concrete example, I'd say that alchemy wouldn't work at all in the canon Potterverse any more than it would in World One. In a badfic that clings pretty close the mechanics of the original, it might be possible for an agent to make it work, but it would destabilize the continuum and exacerbate the issues caused by the badfic. It would probably be less effective overall and require more effort, and the Flowers would be likely to be displeased if they found out. On the other hand, in a badfic that makes major alterations to the Potterverse magic system, or is just so poorly structured that canon in general is being stretched to the braking point, a bit of alchemy would be a drop in the ocean, though a lot of alchemy might make things better, not worse.

In the case of a crossover, the agent would have to follow whatever rules were established by the fic, no matter how bad it is. If it's specifically stated that Ed can't use alchemy at Hogwarts, neither can an agent, even if the logic used violates canon (or is just really, really stupid).

Finally, I don't think that an alchemist agent would be useless just because they can't use their powers. After all, a lot of agents don't have any kind of powers whatsoever, and they contribute just as much. Plus, a character used to relying on their abilities, especially ones as flexible as alchemy, having to cope without them would make for a good story.

As for why, spoilers for anyone who hasn't seen the first anime.




Basically, in the first anime, Edward gets stuck in an alternate reality. Our reality, in fact. And his alchemy doesn't work. Admittedly, I haven't seen The Conqueror Of Shamballa, so I don't know if that was a temporary thing for Edward, but I'm pretty sure it just doesn't work over here. And this is the first anime we're talking about, so it is sort of it's own continuum, but it is also the only adaptation to deal with alternate reality, so I would apply its rules to this situation. Of, course, I have no idea what would happen if an agent got their hands on a Philosopher's Stone, but it would be... interesting. Also, my memory is terrible, so correct me if I got anything wrong.