Yes,unless there is severe weather.
The flyer we received from our hotel states the times on Tue, Fri, Sa, Su, with disclaimers of "Weather permitting' and 'schedule subject to change.' It's free and open to the public. it listed a website for more information.
You can Google search for montjuic fountains to get latest schedules. The do vary.
I think it's year round, but it will end in maybe the year 2020, I think that's what I read. And there is at least one, maybe 2, weeknights that the show happens.
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