Well, they could. But I don't think that would achieve anywhere near the success of the Avengers.
Marvel did a great job with building out their individual characters, making them independently popular, and then bringing them together in a very structured way. Doing it that way meant viewers carried quite a lot into Avengers in terms of information and emotional attachment, enabling them to cut corners in terms of characterization and backstory, allowing that film to concentrate on the dynamics of the new relationships and the action. The film actually doesn't hold up very well if you take it in isolation.
A Justice League movie out of nowhere would struggle by comparison given you'd be introducing so many key characters at once, some of whom the audience has a completely different understanding of e.g. regarding Batman, Joe Average has the Nolan interpretation top of mind. Even if the action, effects, acting and story was on par with Avengers, it would feel much flatter by comparison.
That being said, Warner shortcutting their way to the Justice League movie by riding on the coattails of Superman and not setting up the other League members separately isn't exactly going to be as effective as Marvel's approach of giving the individual heroes breathing space. For example, Batman in this film is going to be in part defined in his relationship with Superman, which may not provide as much insight and interest as building out his character in isolation first.
In summary, I don't think Warner can achieve what Marvel has in only half the time.
I would argue that just getting the JLA movie out the door is more important at this point than trying to catch the Avengers.
The Justice League, as a property, has more cultural awareness than the Avengers did prior to the release of their individual movies. Superman and Batman are the most popular superheroes ever, Wonder Woman is the most popular heroine, Aquaman, GL, and Flash all enjoy their own level of awareness. The biggest reason for doing the shared universe thing, beyond the fact that it's a damn good marketing scheme, is that Marvel's characters didn't have the kind of cache to make the Avengers the kind of success Marvel wanted. No doubt, the movie still could have been big; just not "third highest grossing movie of all time" big. The JLA already has some cache, and even if Supes and Bats (and to a lesser extent, Wonder Woman) have to carry the lion's share of the marketing to get people in the seats (which, let's face it, they'd do regardless), people wouldn't come into a JLA movie with no attachment to the characters.
There's a certain shortsightedness, I think, in assuming that just because Marvel did the superhero team up movie one way that that is literally the only way it can ever be done. Not taking anything away from what Marvel did because it is impressive, but that's giving them way too much credit and not giving nearly enough credit to any of the talented actors and writers who worked on the Avengers and who could potentially be working on JLA. What's really ironic is that this line of thinking - "Marvel did this so everyone has to do this!" - is exactly how executives think and why MoS2 is now introducing WW and Bats and starting the "DDCU" instead of just being a Superman sequel like it really ought to be. And now everyone is bitching about. lol
I also don't think we give audiences enough credit with this stuff. Hollywood has been releasing superhero movies since 1978, with the bulk coming out in the last 10+ years. I think they know how this goes by now that we no longer need to assume not explaining every detail of these characters will send people into some kind spasm in theaters lol. Joe Average, as you put it, managed to accept the Burton Batman after the Adam West era had been a pop culture institution for over 20 years. Audiences managed to deal with Keaton, Kilmer, and Clooney all being Batman in very short time of each other. People know Batman. You can introduce a new actor and people will deal. Unless he or the movie sucks, of course. lol
Which is really the deciding factor. The Avengers wasn't a success just because of the shared universe. That helped, but it was mainly because it was a damn fun movie and one of the most enjoyable theater experiences around.
It's possible to achieve that. Hard, but possible. I refuse to believe there is no narrative whatsoever that could bring together the JLA without setting them all up in seven (remember the JLA is a might bigger in terms of "main" than the Avengers) individual movies first. It's an ensemble piece; the story is about the team. Play up the characters interactions with each other in the story, create a threat that allows them all to show off their individual skills. Get a group of actors with good chemistry and presence. Tell a good story. Film some great action. Make a good film.
Hell, the first League script that was going to get made before the writer's strike started with the League already formed. That would be a fine place to start, in my opinion. We'd lose out on some backstory, but again, the main goal is telling the story of the team. Just as important, the goal is getting the characters out there. Because right now, WB is doing fuck all with 98% of DC's superhero IP.
Would it "beat" the Avengers? Maybe, maybe not. Probably not; the Avengers was lightning in a bottle. Can a JLA movie come out and be enjoyable and do $800 million worldwide (or however much is necessary to justify a sequel and some solo movies for the characters)? I think it could.
It's all ultimately moot since WB has set the course to ape Marvel's efforts. But still