Absolutely! During World War One, at a time before any other form of multimedia entertainment, music and singing was an enormously popular form of enjoyment. While not necessarily designed to aid in work or coordination, soldiers would sing whilst marching, working, while they were in the trenches and more.

Not all songs were written during the war or were even about the war, a popular song amongst British and dominion troops was It's a Long Way to Tipperary whish was written in 1912. Of course, when the war broke out, songs were a popular means for expressing patriotism and for encouraging enlistment. As the war went on, songs were written about different events that occurred, the delay of German forces by the heroic Belgian army is one such example and led to the writing of the popular and quite catchy Belgium Put the Kibosh on the Kaiser. There is also the ballad to the mechanical marvel, the tank called The Tanks that Broke the Ranks. As they war dragged on, the mood of the songs changed with many songs lamenting the conflict and a theme of longing for home emerged. When the US entered the conflict, American soldiers brought with them their own songs such as Over There and Oh Johnny, Oh Johnny, Oh! It is important to remember though that many songs, although written during the war, didn't necessarily make it to the front. Practical radio was still a ways off and many songs were restricted to stage shows.

Additionally to those I've mentioned here, different countries had their own permutations of popular songs which were often changed to reflect a more familiar theme. The extremely popular and well known Mademoiselle from Armentieres had, according to an article I once read, over 700 different permutations many of which were completely obscene in regards to their content.

This website has many of the songs that were popular during the war and you can listen to many of them though they may not necessarily be original renditions. In addition, I recommend checking out a movie called Oh! What a Lovely War which is a comical 1969 movie based on a stage show by the same name which tells the story of the First World War using songs popular during the conflict. Many of the scenes are available on Youtube.

These two books cover this subject very well for WW1:

The Long Trail: What the British Soldier Sang and Said in 1914-1918, John Brophy & Eric Partridge, Andre Deutsch Limited, 1965

When This Bloody War is Over: Soldiers’ Songs of the First World War, Max Arthur, Piatkus, 2001

Certainly for British soldiers in WW1, morale-boosting songs were frequently sung on the march, while working, and while in barracks. They weren't really work songs so much as (often filthy) entertaining ditties. Work carried out in the forward lines (like wiring, trench improvement and sap digging) would usually be done in deathly silence though:

If soldiers sang at all in the front line it was one at a time and under the breath, unless they had reached a tacit and reciprocal arrangement with the Germans opposite. (Brophy & Partridge, p23)

I have read one personal account from the later years of the war that claimed that men in his unit trying to start a sing-along of one of the mawkish popular patriotic civilian songs of the time on the march (like Tipperary or Keep The Home Fires Burning) would be drowned out with booing.

Here are a few examples of (WW1 British) soldier's songs from the above books. These aren't the stirring, proper, patriotic songs that are commonly associated with the war in modern remembrance; they're rude and crude, but this is what the soldiers were really singing:

Charlotte the Harlot

(1914. Marching song based on ‘Gilbert the Filbert’)

I’m Charlotte the Harlot

The Queen of the whores,

The pride of Piccadilly

All covered in sores;

Oh! You should smell me

When I lift up my drawers,

I’m Charlotte the Harlot

The Queen of the Whores.

There is a Sausage Gun

(Sausage gun: a trench mortar or minenwerfer)

There is a sausage gun

Over the way.

Fired by a bloody Hun

Three times a day.

You should see the Tommies run

When they hear that sausage gun

Fired by a bloody Hun

Three times a day

My Nelly

(Air: Three Blind Mice)

My Nelly’s a whore!

My Nelly’s a whore!

She’s got such wonderful eyes of blue,

She uses such wonderful language too,

Her favourite expression is, ‘Bollocks to you!’

My Nelly’s a whore.

Greeting to the Sergeant

(Chant)

You’ve got a kind face, you old bastard,

You ought to be bloody well shot;

You ought to be tied to a gun-wheel,

And left there to bloody well rot.

This might not be quite what you are looking for but there were some quite popular songs among soldiers during the world wars and Im sure someone more knowledgeable knows more about marching songs and the like.

I specifically remember reading about Lili Marleen being very popular among German and Allied soldiers to the extent of which where it was used by the Allies as a way to make German soldiers homesick during the later stages of the war.

Source : ISBN: 9780099539872, The German War: A Nation Under Arms, 1939-45 By Nicholas Stargardt Im not sure there was too much about this specific song in this very book but I quite sure it was mentioned there