Music actually was indeed essential on the battle field for more than 2000 years, and it did massively increase the efficiency of the soldiers.
Once the basic ideas of fighting in formation, unit cohesion, and tactical battle planning were discovered and put into practice (by various peoples, and notably by the Greeks starting with the 8th century BCE), generals began searching for methods to command larger number of troops. Initially the problem was solved by using compact battle formation, with unit commanders instructed to follow the lead of the units near them; but when the Romans introduced the widely open checkered formations which extended the legions over a wide space, a better method of command was searched and found.
[Cornicens -- Roman military trumpeteers -- on Trajan's Column. An officer with the cornicens who are ready to sound their trumpets to broadcast his orders.]
From the 3rd century BCE to the beginning of the 20th century CE, music was the principal method of conveying orders to a large number of soldiers fighting on large battle fields. Trumpets, and drums, and bagpipes, and bugles were used to play simple melodies which carried orders such as advance, pursuit, turn left, turn right, retreat, and so on. Armies which had musical signals had a qualitative advantage over armies which didn't. All soldiers and officers were trained and trained and trained until they understood the musical calls instinctively and reacted instantly to them.
Wikipedia has a list of bugle calls, the last remnants of a once great and varied catalog of musical signals.
Military musicians were protected just like any other soldier, relying on the support of their comrades. They were not expected to risk their lives in the first line, but they were expected to be in the immediate vicinity of the troops during the battle. And they were soldiers: risk is in the job description.
About using women as trumpeteers or drummers: sure, why not. In actual historical practice military musicians were quite often young boys, e.g., the heart-breaking and uplifting story of the 14-year-old Sardinian drummer who sacrificed his leg in the Italian wars of independence, in the somewhat famous novel Heart by Edmondo de Amicis; if young boys could do it, so could women. Whether this would make sense politically and culturally is another issue.