No. That would be "ela trabalha NA galeria", at that place, and not for them
I agree, however, in English, "she works at the gallery" may mean "she works for the gallery", depending on context. I would actually be much more likely to use "at" unless I specifically wanted to highlight that she worked for them but not necessarily at that site. The same would hold true for museums and certain other types of institution.
I work for the gallery. I work at the gallery. Both statements may (or may not) be true simultaneously, but they do not mean the same thing. Be careful of misleading English learners.
I already acknowledged that they don't mean exactly the same thing, however I struggle to think of a situation where I would prefer to say "works for the gallery" over "works at the gallery." I can just about make up a situation, but it is quite artificial because usually galleries have only one site. For companies, it is clearer "works for the bank", but for galleries, museums etc I would almost always say "at".
Here's an easy scenario: "She works 'for' the gallery (as an accountant/lawyer/designer/marketing consultant, etc...)." None of those jobs have to be done 'at' the gallery in question. She could have an office anywhere but work for the gallery.
On the other hand you could say the full time staff, e.g. the curator, receptionist, caretaker, security guard, etc, work "at" the gallery because more or less all their work depends on being there.
I hope that clarifies the meaning of the previous comment. I wasn't trying to put-down or anything.