NO-
 
http://www.forbes.com/sites/insertcoin/2014/07/21/bungie-explains-why-destiny-doesnt-have-cross-platform-play/
 
Bungie engineer Roger Wolfson explained to Digital Trends that it’s a conscious decision they made, not something that’s a technical hurdle they can’t overcome.

“I’ll speak for the hypothetical player,” Wolfson said. “I have a disadvantage sniping across the map because [my opponent with a newer console] is only two pixels on my screen and I’m four pixels on his. You see that in the world of PC gaming, where people are always racing to the best video card to give themselves the advantage.
“Regardless of where the reality is, there’s definitely a perception among gamers that better hardware means you have an advantage. We don’t want to have to enter that fray, so to create the best, most level playing field, both actually and perceptually, we separated it by platform.”