Did Archer Vice happen because of ISIS/ISIL?

In short, yes.

From The AV Club:

Archer drops ISIS name, suddenly finds itself with a bunch of unsellable t-shirts

For reasons we won’t get into here because, c’mon, read a damn newspaper, FX’s Archer has suddenly found itself in an uncomfortable position due to the show’s focus on an organization that operates under the acronym “ISIS.” Speaking at New York Comic-Con—which is like San Diego Comic-Con but everyone’s a bit pushier—Archer‘s cast and crew revealed how the show would respond to real life’s sudden intrusion on the ISIS name. According to co-executive producer Casey Willis, the show is going to drop ISIS as quickly and quietly as it can, with the name being addressed in a “very smart and subtle way” right in the first episode. That comes from the New York Daily News, but The Daily Beast has an actual description of the scene for anyone who doesn’t mind spoiling a little visual gag.

The Daily Beast also reports that the show has scrubbed any mention of ISIS from its upcoming season, and Jessica Walter even re-recorded some of her lines for the first episode to explain that the spy organization now works for the CIA. Matt Thompson, one of Archer‘s executive producers, referred to the real ISIS as “the most awful thing,” and he said the show’s staff “didn’t want to have anything to do with it.” He also notes that South Park would’ve done a whole arc about it, going after the terrorist organization for stealing their name, but in the Archer universe that version of ISIS simply doesn’t exist.

There are some other articles out there. Here's one from CNN and from The Verge.