Do the showrunners consider Supergirl and Constantine to be part of the Arrowverse?

The way they define the term, no; the way fans define the term, yes.

There have been several cases where they producers have used the term "Arrowverse", or have otherwise described the "world" where Flash and Arrow exist. In those cases, they have always kept Supergirl separate.

Early on, in one of the first interviews about Supergirl, Andrew Kriesberg said:

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."

Of course, this was before there were even plans for a crossover. Obviously, those plans changed: the shows crossed over, and they will again. However, the producers still consider them to exist in two separate universes, as in this most recent interview with Kriesberg:

Not for her entire world, but Kara will be traveling from her dimension to our dimension, “our” being the world that The Flash, Arrow, and Legends lives in.

However, it's clear that the producers consider the four shows to be strongly connected in the sense that characters can travel freely between the Arrow/Flash universe and the Supergirl universe. There will be an episode of Supergirl that occurs as part of the Arrowverse crossover event (meaning the same continuous story will take place on all four shows).

Also, we already know that the Arrowverse is a multiverse, and from the perspective of Flash, Supergirl just exists in one of those other parallel Earths (no number, though).

So, for all meaningful purposes, Supergirl is part of the Arrowverse in the sense that you mean the set of shows with shared characters and interactions. It's at least as strongly connected to the Arrowverse as Constantine, for example.

But it is not part of the "world" of Flash or Arrow and there are no plans to merge those two universes together.

According to this quote from Andrew Kreisberg the creator of the 4 shows

As revealed during The Flash-Supergirl crossover last year, Supergirl hails from a different universe. Are you planning on bringing Supergirl into our universe? Not for her entire world, but Kara will be traveling from her dimension to our dimension, “our” being the world that The Flash, Arrow, and Legends lives in.

The SuperGirl's world will remain outside of the arrowverse world.