Is the "Ace" position in Haikyuu just made up for the manga/anime? I've had a look online and can't find any evidence that the term "Ace" refers to a position in volleyball; the only definition I could find was that of a service ace.

Is this term solely used for the sake of the anime/manga or is there any evidence that points to its use in real life?
It's not a "position" in the same sense that "libero" and "middle blocker" are positions. That is to say, you probably aren't going to find any references to an "ace" as a position in, say, the Japan Volleyball Association's rulebook. 

When Haikyuu!! refers to Azumane as Karasuno's "ace", that's in the usual colloquial sense - he's the best (offensive) player on the team. In English, this sense of "ace" seems to be fairly restricted to baseball (where it refers to the best pitcher on the team), but the Japanese equivalent (エース ēsu, borrowed from English "ace") is used fairly often in real life for team-leading players in other team sports as well, including (at minimum) soccer and volleyball.

As it turns out, this turn of phrase has made it way into other parts of Japanese volleyball lingo. A wing spiker (Eng. "outside hitter" or "opposite hitter") who focuses primarily on offense may also be referred to as a "super ace". But this is not the sense in which Haikyuu!! tends to use the term "ace".