Can “Sweeney Todd” pump up Stephen Sondheim’s popular appeal?

With Tim Burton’s movie adaptation of the 1979 tuner gathering enthusiastic reviews and awards buzz, a Sondheim musical now stands to reach its widest-ever mainstream audience. But the man universally acknowledged as the foremost living composer of the American musical has a spotty commercial history, regardless of the critical acclaim heaped on his shows.

If the movie — a challenging, dark period piece starring Johnny Depp as the Fleet Street barber with a habit of slashing his customers’ throats — makes a killing, the current national tour of helmer John Doyle’s pared-down “Sweeney” looks poised to get a boost. So could the upcoming Broadway revival of Sondheim’s “Sunday in the Park With George.”

Whether a cineplex surge for “Sweeney” will win over new legit auds for Sondheim’s entire body of work, though, remains an open question.

Sondheim hardly crafts financial juggernauts along the lines of “Wicked” or “Jersey Boys.” When the 2005 revival of “Sweeney” recouped its relatively small $3.5 million capitalization in 19 weeks, the achievement was trumpeted as one of the rare instances of a commercial production of a Sondheim show making it into the black, joining original productions of “Company” (1970), “A Little Night Music” (1973) and “Into the Woods” (1987), among a few others.

Many of the original productions of critically beloved Sondheim shows were costly endeavors that closed in the red. The 1979 “Sweeney” ran for 16 months, but only paid back 59% of its investment, according to Craig Zadan in his Sondheim survey “Sondheim & Co.” The 1971 “Follies” lost its entire investment, as did the 1976 “Pacific Overtures.”

The popular “Sunday in the Park With George,” which transferred to Broadway in 1984 after a run at Playwrights Horizons, only recovered about 75% of its $2.4 million investment.

Last season’s remount of “Company,” also helmed by Doyle, took home the Tony for revival but still didn’t make it to recoupment over its eight-month run.

Despite all that, Sondheim has an artistic rep that can’t be beat, cultivating a fervent following from his work as a composer-lyricist as well as from other legit landmarks to which he contributed, including “Gypsy” and “West Side Story.”

The generally acknowledged stumbling block to widespread Sondheim popularity is the ambitious intellectualism of his work, with its often challenging subject matter and themes. Take “Sweeney,” for instance; or “Merrily We Roll Along,” the tale of a disintegrating friendship told backwards; or “Assassins,” the unorthodox theatrical exploration of real-life presidential assassins.

“Sondheim shows are quite sophisticated, and Broadway audiences have more and more tended to be tourists,” says Tom Viertel, one of the producers of the “Sweeney” revival on Broadway and the road, as well as “Company.”

“Obviously Sondheim has always appealed to more sophisticated theatergoers than the mass market,” echoes Todd Haimes, a.d. of Gotham nonprofit Roundabout Theater, soon to co-produce the Rialto transfer of Menier Chocolate Factory’s revival of “Sunday,” opening Feb. 21 at Studio 54.

Roundabout also has produced revivals of “Company,” “Follies,” “Assassins” and “Pacific Overtures.” “Our mission is to do great musicals that aren’t going to be produced commercially every five or 10 years, so Sondheim seemed like a logical area for us to explore,” says Haimes, noting that the composer’s offerings have proven strong attractions for both new and renewing subscribers as well as single-ticket buyers. “All of them have been very successful for Roundabout.”

The DreamWorks movie adaptation of “Sweeney,” which opens Dec. 21, seems likely to broaden the show’s appeal, with recent history proving that a screen adaptation (“Chicago,” “Rent,” “The Phantom of the Opera,” “Hairspray”) can revitalize the box office of its Broadway counterpart.

The case with “Sweeney” is more complicated, since there is no Broadway incarnation currently playing to reap the movie’s B.O. rewards. However, the Tony-winning 2005 revival is on the road, with recent stints in Boston, Toronto and Columbus, Ohio, soon to be followed by a further 17 stops through June, including Miami, Dallas, Los Angeles, Chicago and Atlanta.

Viertel anticipates the movie will steer new auds to the road production.

“I do expect to see a lift from this, but it’s an interesting question,” he says. “This is the road, where engagements are shorter and people’s ability to plan ahead with single-ticket purchases is limited. But just the rise in exposure to the title can be valuable.”

Haimes thinks a new awareness of Sondheim’s work also could fuel “Sunday.” “There’s ample evidence that the success of a movie musical will help a legitimate production,” he says. “In terms of having a really long life for ‘Sunday,’ the movie could help.”

That is, of course, if the pic proves a hit — no small feat for an R-rated, Grand Guignol musical that graphically depicts every single one of the multiple throat-slittings perpetrated by Depp’s vengeful barber, abetted by his doting accomplice Mrs. Lovett (Helena Bonham Carter).

One of the first steps in marketing the film was to win over notoriously picky Sondheim avids — a mission that seems to have been accomplished, judging from the positive buzz generated by a Dec. 2 Gotham screening for Broadway industry regulars. At the event, Burton and Depp were trotted out and Sondheim got up to voice his support for the pic.

“It would be foolish to dismiss Sondheim’s power,” says Terry Press, marketing consultant for “Sweeney.” “These days, because information travels so quickly, if ‘Sweeney’ hadn’t been embraced, the mainstream media would take that and go.”

The movie aims to attract an untested overlap of Sondheim fans, Burton acolytes and Depp lovers. Burton and Depp have collaborated on past hits (“Edward Scissorhands,” “Charlie and the Chocolate Factory”), while Depp has his own legion of supporters from the global success of the “Pirates of the Caribbean” franchise.

So far — thanks to Depp, Burton and the promise of blood — the pic is tracking especially well with young males under 25, hardly the usual demo for Sondheim fans (or for musical theater in general).

If younger auds drawn to more violent fare do turn out specifically for “Sweeney,” they won’t necessarily be the same people who embrace the wider range of Sondheim work about, say, a young New Yorker’s fear of commitment (“Company”) or an artist’s process (“Sunday”).

Still, box office bounty and trophy wins for the “Sweeney” pic could at least set the stage for the barber’s legit return to Gotham — a move made even easier with an existing production already on the road and able to shift fairly seamlessly back onto Broadway.

“We haven’t looked at that seriously, but certainly we’re poised to do so,” says Viertel. “If the movie takes off, I’d kill to get ‘Sweeney’ back to New York.”