To the extent that the Brownstone getting wrecked up has anything to do with a stipend, it would, I would say, argue against it - if one is handed out, the Brownstone repairs would come from the same pool of funds (by all indications, from Wesley Dodd’s former fortune) as the stipends, and Ma Hunkel’s salary.
As to their employment or lack of…Stargirl, Cyclone, Jakeem Thunder and Lightning are all students, so presumably their parents (or other guardian, in Jakeem’s case) support them.
Several of them are relatively wealthy - Green Lantern, Flash, Hourman, Liberty Belle, Sandman, Wildcat, Mr Terrific and Power Girl all founded, or are the heirs to the founders of, (relatively at least) successful businesses…PG and Wildcat are, AFAIK, the only ones who don’t currently own said businesses (well, Hourman’s dad is probably still in charge because of his non-death), though I’m unsure of the current status of Quickstart Enterprises and Garrick Labs. (And ISTR mention of the upcoming Power Girl series involving her having a secret identity and owning the business again.)
Obsidian is presumably still employed by Kate Spencer’s former law firm.
Lance is employed by the US military.
Dr Mid-Nite has a presumably lucrative sideline, aside from his superheroing, and running his free clinic, as a medical consultant.
Adult members known to be otherwise unemployed: Mr America, Judomaster, Starman. Though Starman’s place of residence when off duty being a mental hospital means he probably doesn’t need money.
Adult members with unknown civilian (er…odd choice of words, I guess) job status: Amazing Man, Damage (he’s probably unemployed), Hawkman (he was employed in a St Roch museum until he disappeared in the last Crisis…currently, God - or Geoff, I guess - only knows.)