It doesn't seem to have been properly evaluated, and from what I can tell it's primarily argued to be a study help and programmers.
The Pomodoro Technique for Sustainable Pace in Extreme Programming Teams has an analysis of it being used while doing XP (Extreme Programming). However the paywall is making it hard to access their analysis, but the slideshare from the authors make no mention of productivity, so I believe that it's purely been used as a way to structure work.
The inventor Francesco Cirillo has written The Pomodoro Technique (The Pomodoro) a fairly thick manual, but he's not citing any studies for his claims about productivity. It instead appears to be well reasoned manual with some anecdotes, but with little supporting evidence.
I also think that when you ask a question about the pomodoro technique, it's important to also ask; "As opposed to what?". The pomodoro technique forces you to become organized and do timeboxing. It also introduces discipline into the work process by advocating that unit work are atomical, and that you have to finish it before you get to do a break. If you are completely disorganized, then just about anything reasonable should improve your productivity.
As a last resort I tried looking up research that shows organizing your work leads to productivity gains, but I can't find anything directly looking into structured work vs unstructured work in terms of productivity. Maybe for the same reasons we can't directly answer Is the use of parachutes supported by peer-reviewed papers?.