No it won't. They will be boosted to a higher level of course but they won't be demoted their division. The only way that can happen is if they are inactive for a few weeks they will decay or they lose like 10+ games in a row.

The only thing is if they are out of their skill level all that happens is they get stomped on. Usually people buy high elo for these reasons:

• You get rewards for being high elo
• You get to boast to your friends
• I shit you not but there is a facebook group (league of hunnies) where if you are a diamond or higher player...females will just sleep with you just for being high elo. (I am not lying)