No more than being an infantryman in the front rank was suicide; when infantry formations were loosing volleys into each other, there was basically nothing an individual soldier could do to defend himself. With the smoke blocking his vision and stinging his eyes, there was no way of knowing which enemy soldier was most likely to kill him, and with such inaccurate weapons, no way to shoot him first. His best chance of survival was fighting in concert with the unit, loading and firing at a steady pace until the order was given to charge home with the bayonet. Even then, though, the soldier would rarely actually come to grips with the enemy, having forced them to flee rather than stand around and be bayoneted.

Here, the musician probably contributes more to the unit's success, and thus his own survival, than any individual musketeer. By providing a steady rhythm, he helps shore up the unit's morale, aids in the disciplined execution of drill, and does what he can to prevent the unit from running when under attack or splintering when charging into enemy fire. One's chance of death at any moment was still essentially random, but good musicians could improve the odds by helping their unit beat its opponent.

A related question: Was it considered dishonorable shooting a musician?

No, because infantry rarely engaged in melees within physical reach of each other, which is when you'd need a weapon to defend yourself. Mostly they closed to musket range and engaged in firefights - a musician was no more vulnerable than any trooper of the line to musketry or artillery. Even a bayonet charge rarely led to significant amounts of melee combat; one side would tend to break and run when the other charged. The exception would be when they were defending an obstacle (such as Hougoumont at Waterloo), and on such occasions there could be extensive hand to hand combat. Musicians were unlikely to take part in them, or if they did they could pick up a dropped weapon. Given that they were quite often young boys, they were also extended mercy - the British troops at Hougoumont spared a drummer boy who was trapped alongside several other French soldiers after breaking into the compound. They killed all the others.

It's not quite the same but there were Bagpipers who walked in front of the troops during WW1 and 2 -possibly other wars too - the Germans said they didn't shoot at the pipers because they thought they were mentally ill.

I'll look for a source but this is what I remember reading

edit: src: http://www.historic-uk.com/HistoryUK/HistoryofScotland/Scottish-Piper-War-Heroes/

During the Napoleonic Wars, this role was often filled by children (hence "drummer boy," "bugle boy," etc.). Their primary task was to convey commanders' orders, but they were also charged with other tasks such as caring for the wounded. They were therefore typically either with the colors or in the rear ranks. Although battlefield musicians have been depicted marching in the front ranks in several paintings by contemporary artists (who did not witness the battles they depicted), I've never read of them being placed in the forefront of a battle formation. Given the range of weapons at the time, anyone on the battlefield was at risk, but being a musician would not have been considered suicidal by any means.