Is there any form of cross-play with X, Y, Omega Ruby, or Alpha Sapphire?
Thanks in advance!
As far as I'm concerned, there are no plans for the future of cross-play, at least not something they announced.
There are, on the other hand, some declarations that were made from Nintendo that "they would like to add cross-play with Pokémon Sun & Pokémon Moon" but I assume they will decide to do it or not depending on the amount of people playing when the summer is over.
If I find the original interview where they said it, I will edit the answer to add some links.
EDIT: It seems that the team responsible for this project said in the E3 that they had the plans to tie-in both the new gen games and Pokémon GO:
"While explaining the uses of the GO+, the team also revealed that Pokemon GO and the GO+ will eventually tie-in to Pokemon Sun and Pokemon Moon. There was no explanation about how this will work at this point in time."
I still think that it will depend on the player base at the end of the summer, but we will see eventually.
There have been no announcements even hinting at this as a possibility, but other factors make this seem highly unlikely.
The underlying mechanics regarding stats and possible moves are completely different and would be difficult to translate from PoGo to the main series or vice versa.
Pokemon Go is made by a different company than the main series installments.
Short Answer: There isn't so far.
What Niantic is going to implement is speculation, but they might bring the Pokémon like in series: So far Gen 1 (1-151), then Gen 2 (152-251), but there is no official statement about this.