Recently I decided to start watching the TV show Arrow, and recently made it to episode 5. While watching, he looks at his friend-turned-partner Digs, and says "You know us billionaire vigilantes--we do love our toys." Does this mean that he is aware of Bruce Wayne's activities as Batman, possibly inspired by them? Or is Queen just being a wiseass?
It's not a coincidence, but it's not an in-universe reference. It's an "inside joke" of sorts.
Stephen Amell has gone on record multiple times as saying that he tries to get the writers to work as many DC references into his show as possible. There are limits to how much they can get away with, because the Batman properties are licensed elsewhere, but they still name-drop Superman or Batman (or others) when possible. Some times they make it into the show, sometimes they don't. Examples include:
- In an early interview, Amell says he tried to work a line into dialogue soon after his return, where he waves to someone off-screen and calls them "Bruce", implying that he and Bruce Wayne are friends. (It didn't make it in.)
- In the Legends of Tomorrow premiere episode, Rip Hunter talks about both "dark knights" and "men of steel"
- Felicity's code name is Overwatch because "Oracle" was taken. Oracle is the code name of Barbara Gordon, former Batgirl, who was crippled by Joker and is in a wheelchair.
The show's dialogue is written in such a way that Batman "probably does" exist in Gotham somewhere, but they can't say that. So whenever they can, the writers insert these kinds of remarks as a wink-and-nod to the fans, to let us know that the show does still exist within the broader DC universe.
Is it an in-arrowverse reference?
...Arrow and Flash executive producer Andrew Kreisberg stressed that anything you see referencing Batman on the show is “a tease.”
Explained Kreisberg, “Obviously, they have the Batman movies and there’s [the series] Gotham. DC are amazing partners and Geoff Johns, who’s the chief creative officer [of DC] and one of the developers of Flash and done episodes of Arrow, he’s been with us from the very beginning on both shows. There are things we can do and things we can’t.”
Kreisberg noted, “I’m a huge fan of Nightwing,” and how exciting it was for him on Arrow “Getting to name check Blüdhaven and go there.” However, he said there are still restrictions in place even when it came to mentioning locations, adding, “There’s the cities that we can use and then there’s everything else. I don’t think you’re going to be hearing ‘Gotham’ or ‘Metropolis’ [on Arrow or The Flash] anytime soon.”
That said, since that article, there have been references to Wayne Tech in Flash (in a possible future).
Plus Supergirl (with Metropolis and Superman) is now part of the Arrowverse but only (AFAIK), as a separate part of the multiverse* and does not exist in the same universe as Arrow/Flash/etc.
*These universes/multiverses are a tad confusing
So, the original stance is softening
Absolutely the script has a nod to Batman but the Arrowverse does not include explicit canon knowledge of the Bat-verse yet. Thus Oliver wouldn't know about Batman / Bruce Wayne yet.
As mentioned by @JasonBaker...
In fairness, this doesn't mean there isn't a Batman, just that they can't explicitly mention him on the show.
It's a fourth break wall, and a wink to the audience. There are two main reasons why there's no explicit Batman in the Arrowverse.
1. Copyright stuff
You know, the basic stuff. Batman is not part of the contract, so he can't be shown or mentioned, nor can be any of the related characters/places. Very similar to the MCU movies not being able to even use the word mutant because the X-men currently belongs to Fox.
You know, all the great stuff Paulie_D's answer mentions :)
2. Arrow is already Batman
I mean... in the arrowverse, Arrow has been given a lot of Batman's plot lines (being chosen by Ras'Al'Gul, marrying his daughter, forming his "family" of vigilantes, getting (one of) his love interests paralyzed by a villain... actually that Overwatch/Oracle reference was oddly specific (the only difference being that Overwatch/Felicity was the tech-comm-Cisco-person already before the accident)
So... even if some day they could get the rights... there's not much they could do with him, since they've pretty much turned Arrow into Batman. Yeah, he doesn't have the alfred, or the cool bat motives or the Joker, but... they've given Oliver all the "batman stuff" they could so there wouldn't be much room for a redundant character.
Actually I wonder if in that hypothetical case, they'd give Batman some Green Arrow plot lines...