In literal context yes. When a band plays a song together, simultaneously, it is played live.
But personally, I find a soundcheck not a real performance, and not real enough to fit in the context of this topic. A soundcheck doesn't give much credit to the song itself. I even find it a cowardly move. It's double faced. Either have the guts to do it, either don't do it, but don't fool around and record it with uninterested faces (like Priest did). If Maiden would record Alexander the Great with cameras, prior to the Las Vegas show or whichever other one, release it and then say "yeah, we felt like doing that but we're never going to play it for you guys, this is it.", all hell would break loose. That's like acting to give a kid a cookie and as soon as the kid grabs, the cookie is withdrawn and eaten by the giver himself, a la cookie monster. I'd say: better not fool around, and don't show that cookie at all.
I even think bands could 'stage' something to make something special by picking a song on purpose that won't be in the setlist. By playing (after the selection) it in a soundcheck, they suddenly "created" something special and release it as a bonus, or if worse: they could make the fans pay extra for it.