League of Legends (LoL) Question: Can i climb Gold elo with AP Trynda ?

You can totally climb, as long as you have a good build and a lot of practice with him. There are a lot of things like AP Trynd that people play even though they aren't in the meta, and they do well. They won't have a problem with it unless you do bad with him.

you won't get banned for playing badly - You only get banned for attitude.

It is tough to play AP Tryndamere, but if you're good enough at playing him, you can do it.

Sure, play him. You won't get banned for it even if you're reported if you haven't done anything reportable. Ap trynda is not exactly the best champion to climb elo but go for it if you like it.