It very possible to use the environment to your advantage as you are suggesting, but you have to be careful about how you word it, and/or which move you use and/or which Pokémon you ask to do it. I can see a Scizor slicing through a tree with Cut/Metal Claw etc, but I can't see a Cleffa doing any damage to a tree that is sizeable enough to make it drop and cause good damage on the opponent.
You then have to think about the fact that it's a falling tree and can be easily avoided given the right set of orders and/or circumstances.
However, to answer you question simply, then yes you can do that.
Don't be disheartened with not knowing much yet. This is why when you start, you get more and more experience through battles and get to laces like where Jeri and myself are. Also, if you intended the message that I see on your VM page for me, then next time I suggest pressing the "View Conversation" button first.
Also, we always relish new people and new ideas, as yours were good and Jeri liked them as long as they weren't unbalanced.
Hi and welcome to the ASB. Just a note, I see you have listed your squad as a main squad and a backup. If you intend to bring all of the main squad to your battles every time, you will have an issue with having both of you level-ups in the same battle as they have a habit of disobeying you. Instead, choose to only bring one of your level-ups when you have a battle.