Does crimson spread in the mobile edition?

No known bug causing Crimson not to spread is recorded for any platform.

In Normal Mode, Crimson spreads through grass across dirt blocks, requiring direct contact from other Crimson grass or a thorny bush. This includes growing new Crimson grass or converting existing grass into Crimson. Before Hardmode, Crimstone and other forms of Crimson do not contribute to its spread, and cannot convert nearby grass. The spread of Crimson can be stopped by Sunflowers, just like Corruption. Also, Crimson will only spread while the world is active; it won't spread while the game is closed, a different world is open, or while the game is paused.

Source: http://terraria.gamepedia.com/Crimson