If the Latin alternative band La Santa Cecilia wins a Grammy Award on Sunday for its album "Treinta Días," it will have a long list of shout-outs to bestow.

To the merchants of Olvera Street, who remember when the band's lusty-voiced lead vocalist, Marisol Hernandez, was a little girl crooning Spanish-language boleros for spare change.

To Los Prietos Boys Camp for young offenders, near Santa Barbara, where the band played a free gig earlier this month for the boisterous juvenile wards.

"They're like, 'If you win, you'd better not forget us!'" said Hernandez, a.k.a. La Marisoul, who sings like the love child of Janis Joplin and Celia Cruz and dresses in a style that might be described as Mesoamerican-Tropical Pop art (polka-dot blouses, lemon skirts, hand-painted shoes).

FULL COVERAGE: Grammy nominations 2014

Last year, as La Santa Cecilia's identity evolved from L.A. hometown sweethearts into the musical face of the country's fast-growing under-35 Latino population, the band found new friends across the country. Band members also turned into melodic cultural emissaries in the debate over immigration reform, performing at rallies nationwide.

The kitchen crew at Pat's restaurant in Philadelphia showered the group with free cheese steaks in gratitude for its hit single "El Hielo (ICE)." The song, despite its chilled-out bossa nova tempo, is a fiery cri de coeur about three immigrant workers living in a fearful twilight zone of the American dream.

La Santa Cecilia fans know that one worker is modeled on La Marisoul's mother, and that the band's accordion player Jose "Pepe" Carlos was 6 when his Oaxacan parents crossed the border illegally. He's been fighting for U.S. citizenship ever since.

"This year, we've been able to go to places like Charlotte, N.C., Washington, D.C., Chicago, throughout Texas, and everywhere we go the people that come out are people like Pepe that are going through all that same stuff," said percussionist Miguel Ramirez.

But whether it takes home the trophy in the Grammys' nebulously designated Latin rock, urban or alternative album category, La Santa Cecilia — a local favorite since it began playing to wall-to-wall dance crowds at La Cita and the Echoplex in the mid-2000s — already has savored the kind of breakout year that can turn an emerging act into a headliner.

TIMELINE: Grammy Awards through the years 

Mainstream culture certified La Santa Cecilia when the trade publication Advertising Age last year named it one of the "Rising Hispanic Artists to Watch," citing the band's "crossover appeal" from the Spanish-dominant to the English-speaking general market and the great in-between.

Although the band, which also includes Nicaraguan bassist Alex Bendaña, sings mostly in Spanish, its sensibility is as casually multicultural as the signage at an L.A. mini-mall.

"They definitely became sort of like the voice of immigrants," said Mariluz Gonzalez, a promoter and manager who co-hosts the Latin alternative radio show "Travel Tips for Aztlan" on KPFK-FM (90.7). "It just came at a great time and it resonated with a lot of people. It got them out of L.A. and kind of made them into a band that has national appeal."

One recent afternoon, the band gathered at the San Fernando Valley studio-home of producer Sebastian Krys, a native of Argentina who has worked with pop stars Shakira, Carlos Vives and Gloria Estefan. All the band's members, who are in their early 30s, still make their homes in L.A., where La Santa Cecilia formed years ago when La Marisoul and Carlos met while performing on Olvera Street.

PHOTOS: Grammy nominations snubs and surprises

The group, which is named for the patron saint of music, was offering a reporter a preview of its followup to "Treinta Días," the band's major-label debut on Universal Latino. The new disc is due out this spring.

The untitled record's opening track, a cover of "Strawberry Fields Forever," typifies La Santa Cecilia's canny musical ramblings. It commences with the celestial pluck of a jarocho diatonic harp, picks up speed with a vaguely samba beat, then adds a psychedelic norteño accordion line that in context is as weirdly groovy as John Lennon's facial hair.

The rest of the album pivots from the flamenco-esque "La Morena" (including samples of Olvera Street ambient crowd noise) to a jaunty '60s-retro pop tune ("Someday Someday New") and a smoky rendition of "Cuidado."

"One of the first songs I heard as a kid," La Marisoul said of the classic José José tune. "I remember riding on the 10, in my dad's car, and him having tapes. And he's like, 'Hija, escucha este.' One of those first songs that you get to bond with your parents with."