Yes, they have, though the spelling seems inconsistent.
Yes. When discussing Supergirl early on, Andrew Kreisberg (a producer on all the Arrowverse shows plus Supergirl) used the phrase, though he hyphenated it:
And quite frankly, just making the Arrow-verse, which is what we call Legends, Flash and Arrow work and then making Supergirl work, it's enough of a challenge without having to add a fourth player." src
Most other media outlets have been using the term since Flash premiered, without the hyphen, and the showrunners seem to have been going along with it. For example, during the promotion for the introduction of Vixen to the CW Seed online network, Mark Guggenheim (who is one of the producers of Arrow, as well as a long-time writer for DC comics) retweeted a bleedingcool.com story:
The Arrowverse Grows As The Animated Vixen Series Is About To Begin src
Guggenheim himself later repeated the term "Arrowverse" in a promotional Video for Vixen
"Vixen. An animated series that takes place within the Arrowverse"src
It's obviously impossible to tell from the spoken word how to "spell" it, but he seemed to say it as just one word, not two.
As @cde points out, the showrunners have also used the term Flarrow to describe their universe, e.g. when discussing the first big two-part crossover:
#Flarrow storyboard glimpse src
It's here! The #Arrow and #TheFlash CROSSOVER tonight at 8/7c! Bigger! Faster! Arrow-y-er! So excited for you all to see! #FLARROW src