In League of Legends, there are seperate Elo scores for each gamemode's matchmaking. This means that your ranked Elo is seperate to your standard (normal game) Elo.
When going into Matchmaking, the matchmaking system uses the Elo that corresponds to the gamemode you're queuing for.
Because Ranked games and standard games are considered two different gamemodes, they have two different scores.
(ie. You have 1000 Elo (it's an estimate, we don't actually get to see this value) in standard games, and 3000 Elo (this value is visable in your Ranked stats) for ranked games on Summoner's Rift. This means that your next standard game will be against those that have a lower skill-level than you, while your next ranked game will be against those that are the same skill-level as you.)
As far as the matchmaking system is concerned: Your ranked Elo (MMR) does not affect the standard Elo (isn't taken into consideration during Standard Game matchmaking).
The point is: Even if you're the top player in Ranked games, and you've never played a single standard game (not possible, since you HAVE to play Standard Games to be able to level up), you will be matched with those close to the starting Elo if you were to play a Standard non-ranked match. The matchmaking system does NOT care about your ranked stats (MMR, Elo, etc.) if you queue for a Standard non-ranked game.
The only thing that will be taken into consideration is your loading screen portrait, which reflects the current league you're in.