[2019] Dota top 500 Carry player trying to get challenger in a month.

(As a player, not a staff member)

I think it's really unlikely unless you absorb information like a sponge. There are some things that transfer over from DoTA and others that don't.

I play this game a lot - 5-6 hours a day on weekdays after work is not uncommon. Lack of time investment is not what keeps me from climbing to the upper echelons of ranked (high diamond+), but the fact that I don't learn from my mistakes/absorb information enough and am able to turn that information into better plays. That's not to say that you will have the same experience I do, but I imagine my experience is quite common.

I think it's a really tough ask to be able to reach top 500 of a given server (unless you play on a really unpopulated server) just due to your past experience in other games unless you're able to learn the meta and strategy of league really quickly and adapt to your mistakes, bearing in mind you'll be competing with people who likely play League as a job.

Still, I wish you the best of luck in your attempt :)

Is buying accounts okay in league or something?

No. :P And my comment was assuming you had a level 30 account. I think it would be impossible without one.