There is one way.
However, it is very hard.
You probably will not get it. Unless you have friends in high places.
In Japan, there is an event for a Shiny Jirachi, running from Dec. 1, 2014 to May 28, 2015. Here's what Serebii has to say:
>Location: Pokémon Center - Christmas Charity Wristband Promotion
>Type: Serial Code
So to answer your question, yes. There is (technically) a way to get Jirachi in the PokéDex, but it will be very difficult.
TL;DR Technically, yes. Practically, no.