Yes, in fact, almost half of the high elo players play what they enjoy and that is the best to play league in my opinion. Many of the players play something like Udyr jungle or Janna which is not at all meta, yet they still achieve the highest rank.
Yeah, of course u can, just get better on macro and micro gaming and get better with 2 champions u like to play it. The most important thing to get stronger is reach a good farming, there are many non-meta monochampions who reaches master or grand master.
i mean if your skill proficiency in a single champion is very high you can climb without being meta since you have a greater understanding of what your champion can and can't do in situations. allowing you to play smarter and out play others