I get the feeling they did look at the original comic book story for DoFP or, at the very least, Claremont explained it to them. And clearly they looked at the comic for The Wolverine. Also, they must at least have looked at the comics for First Class (with the final design of Magneto's helmet, Banshee's glider/wings/cape and even Magneto's raising of the submarine).
But in the past, not so much. It feels like they ignored the comics and even the cartoons for the most part. Otherwise we wouldn't get Jubilee making electrical charges (in the deleted scene for X2) rather than plasma baubles, the total absence of a firebird for Phoenix in X3, etc.
It certainly wouldn't hurt them to study the comics a bit more for background on some characters (Storm being the classic example). There's no excuse for not having a bit more of an idea about how characters fit into the mythos, and what their place and significance is within X-Men lore. Storm has been in the comics for 38 years - that's a lot of source material for reference and inspiration. Havok has been in the comics for 44 years. Scarlet Witch has been in the comics for 50 years.