Do shiny Pokémon show as shiny on the map?

Since March 22, it has now been confirmed that at least the shiny Magikarp and Gyarados have been introduced in game.

If a Pokémon is shiny, would it appear as shiny on the map, or is it required to launch the battle to see if the Pokémon is a shiny one?

A shiny Pokémon won't appear as shiny on the map, and will just keep its normal colors. So you do have to launch any battle to check if the Pokémon is a shiny one or not.

As confirmed in this article:

You’ll want to make sure to catch every single Magikarp and Gyarados you see if you don’t do so already. After all, you won’t be able to tell whether the given Pokemon is shiny by looking at your map and nearby tracker; the Pokemon will appear normal colored on these screen and will only reveal itself to be shiny during your battle.

It is also confirmed by some users in this Sylph Road Reddit thread:

I just caught a shiny magikarp, it wasn't shiny on the map and only showed as shiny after I clicked on it. It wasn't shiny for anyone else, either.

Or:

Nope, until the encounter triggered it looked like a regular Magikarp