Is it possible to reroll skin shards into a skin you already own?

Re-rolling 3 skin shards into a permanent will always give you a skin you do not own.

In the case you own every skin, it just re-rolls into a random skin and unlocks nothing.

https://support.riotgames.com/hc/en-us/articles/207884233-Hextech-Crafting-Guide

Chests are random, and can contain content you may already own.

We're looking at features to allow you to use the duplicate shards in various ways. For now, you can re-roll shards to guarantee a piece of content you don't own, or you can disenchant already-owned shards to help you create permanent content from shards you don't own.