I can almost guarantee that it's not a possibility simply because of legality issues if we're talking actual concepts. The only way around it would be to hire the artist as a freelancer and even then it would have to be a new concept they haven't already done outside of Riot. I doubt Riot is willing to hire everyone who enters the contest, even if only for a month.
If we're talking just ideas, then we're still gonna run into the issue of this being the internet. You can 100% be sure that the top results would be like "Gushing Granny Annie", "Hitler Did Nothing Wrong Udyr" and "Robot McRobotface Blitzcrank". That means Riot would have to limit what our options are, and then what's the point? Riot already knows what sells the most, so why would they ask us when our wallets have already spoken.
You might say Star Guardian Urgot, but I'm willing to bet 99% of the playerbase don't want an Urgot skin because they don't play Urgot. And if they do, they might not want Star Guardian Urgot, they might want Dreadnova or Elderwood Urgot.
All this poll is gonna lead to is champions like Riven, Yasuo and Ahri getting more skins because they're the most popular and people want more skins.
It's a really good idea in theory, but being the pessimist I am I can say it's most likely way more trouble and work than what it's worth for Riot.