Largely unlikely, especially within British regiments. I will use the Dorset Regiment as an example. Comprising of 12 Battalions, which was actually one of the smaller regiments during the war, some regiments, such as the Kings Regiment (Liverpool), contained 49 different Battalions at points in the war.
The likelihood would be that men enlisting a year apart from each other, would be that they would be placed within different Battalions. Dorsetshiremen saw service throughout the world, Battalions were sent to France, Mesopotamia, Egypt, Palestine and India, as well as garrison duty at home.
The losses suffered during the war by the regiment were high, for example, at the Siege of Kut, the 2nd Battalion had 350 men captured, only 70 of which survived captivity. Further to this, the surviving men of the 2nd Battalion were amalgamated with the 2nd Battalion the Norfolk Regiment to form the 'English Composite Battalion' which as you can see, reduces the chances again that those enlisting would meet a friend at the front within the same battalion.
With high losses, and the number of battalions, the reunification of childhood friends were pretty slim due to the global nature of the war, along with the sheer number of men fighting on the western front. the 12 battalions lost 4060 men during the war, 6 battalions never actually saw combat. The question you asked specified meeting another man at the front, and on average, each frontline Battalion had roughly 680 men killed, not accounting for the men who left the Battalions due to injuries, it would therefore be unlikely that you would meet. The slim chances would be reduced even further when looking at the larger regiments.
I hope I have been able to provide you with a helpful answer!
Any follow up questions are encouraged!
Sources:
Braddon, Russell, The Siege, (New York: Viking Books, 1970).
Knight, Paul, The British Army In Mesopotamia: 1914-18, (Jefferson: McFarland, 2013).
Popham, Hugh, The Dorset Regiment: The 29th/54th Regiment Of Foot, (Barnsley: Leo Cooper, 1970).
Simkins, Peter, Kitchener's Army: The Raising Of The New Armies, 1914-16, (Manchester: Manchester University Press, 1988).
It really depends on the country, regiment, and what the two men were assigned to do. If you could be a little more specific in your question, I can see what I can dig up.