The answer to this is unfortunately a "we don't know".
This thesis "Music listening in UK offices" which goes into fantastic detail and well worth the read on this subject.
They conducted three studies and the conclusion was that music meant different things to different people and people had different reasons for listening to the music, but those people felt it important to have.
Across all three studies, the findings present a varied picture. Music
could be distracting while working, but could also help to manage
other distractions in the office environment. Music could be relaxing
when employees chose to listen, but annoying when imposed. Even though
music was subordinate to work activities, it was nevertheless
important in many different situations, for many different reasons.
This study is quite thorough and detailed and I think the study itself and the conclusion is typical of the results you are likely to find: music means different things to different people and people relate to it in different ways - good luck in trying to put something so subjective down on paper!
There is this study from 2005, which was only on approx. 50 software developers:
Results indicated that state positive affect and quality-of-work were
lowest with no music, while time-on-task was longest when music was
removed. Narrative responses revealed the value of music listening for
positive mood change and enhanced perception on design while working.
There is also this study on 70 I.S students:
One-way ANOVA results indicated a statistically significant difference
in anxiety level between control and music groups with the greatest
difference following the initial music listening. Repeated measures
analysis revealed the least amount of anxiety level across time for
the periodic group.
What is also evident from the bits and pieces around there is no conclusive evidence to suggest a massive increase or decrease in productivity, however music does provide a level of personal comfort and enjoyment. So the benefit isn't weighable by the employer, but there is a perceived level of satisfaction by the employee.