Fair disclaimer: I've never played one of the GC games. I only know some things about XD plot-wise. I am also not a saturday morning Pokémon villain, nor have I played one on TV.
I'm pretty sure tho, that Shadow Pokémon are described as Pokémon whose "hearts are closed", and that whatever that is intended to mean is mostly portrayed as the Pokémon having 1.- its natural power throughtput / potential uncapped (not much unlike Mega Evolution, I'll come back to this later I swear) and 2.- its self-awareness or ability for conscious thought and decision making completely removed (not much unlike Movie 4's Dark Pokéballs).
Now, how much does this effect the environment? On an environmental scale, the truth is, not much. Not even in the case of eg.: Shadow Lugia. See, regardless of the canon we're coming from, anime, games, whatever, one thing that is put there very clearly is that Pokémon already have a tremendous ability to interface with their environment, not only including high directed elementalism (pyrokinetics, ground and psychic sensing, ability to coerce vegetation, etc) but also ability for control of weather and related phenomena in the local size and scale in the least. Moves like Sunny Day, for example. And let's not even think of what a move like Trick Room does to the laws of physics and causality in a local scale.
So, uncapped, Pokémon are already very powerful. The only practical difference between a random Route 122 Trapinch and say the local Groudon is the scale over which they can exert their power - from a couple of meters around, enough for a battle, to geological mesoscale, enough for what should have amounted to a hemisphere-wide environmental crisis - but nooooooo, all we got was a little cutscene of them going "bump bump wiggle wiggle" at each other, then space gecko. This I mention is important: for all the power Pokémon are supposed to have or at least be capable of, the franchise shies away of showing that potential or its consequences in any form except in some of the anime movies.
So... Shadow Pokémon. Here we have a creature that is a Pokémon forced to exert its maximum power at all time, and removed from the ability to decide that they need to rest, settle down, or even choose their targets. The games do mention at times IINM that these Pokémon are so powerful and unhindered that after a given time of confrontation they automatically resort to self-harm. If you think about that... it makes sense, after enough time of being twisted into persistent, uncontrolled entomokinetics (ie.: Bug-type stuff) your body is going to be tired and asking for a release. So before that time you might have already managed to wreck a couple of buildings, poisoned a river's current, perhaps snap a couple of trees off their roots and throw them downhill from a random mountain, and flooded a small town with a Rain Dance, but... is that any much different than what you could have already done otherwise?
And let's remember not only Shadow Pokémon an uncommon occurrence (phew!) but also after the damage they have dealt, other wild Pokémon (not to mention Trainers, Rangers and stuff) would likely chime in to help repair the damage, as it has already happened in the anime a couple of times.
tl;dr: Shadow Pokémon are very powerful, but barring something like a Shadow Groudon or other high-tier elementalist Pokémon, they are likely incapable of dealing lasting environmental damage over a well-defined area and period of time.
As for battles... given the two numbered points I brought up before, sending a Shadow Pokémon out for a fight is an implicit acknowledgement that you don't care about rules or the result of the fight. You only (and mostly) want the other guy dead. You can not guarantee control of a Shadow Pokémon. You can not guarantee the targets it chooses. You can not reasonably account for colateral damage and I'm pretty sure you can not reasonably prevent them from turning on you for the lulz. It is, the way I see it, the ethical equivalent of a cop or a thug going for a gun: an implicit acknowledgement that you no longer care about the result beyond wanting someone dead - ideally "the other guy" but you have just rescinded your right to secure that choice.
