I can't find any war diaries for these units on line (WW1 war diaries are available on line at the following link)
This doesn't mean there aren't any. Sometime's war diaries of units got "mixed up" with others, or if the Units name changed (which happened quite a lot) or the unit was amalgamated with other units, their war diaries would be "rolled into" the other units.
Also, War Diaries, were only required to be written by units when they went oversea's. Many did them anyway, even in Canada......but other's didn't.
My suggestion, again contact LAC and see if they can point you in any direction to find out information on No 2 Canadian Army Service Corps Service Company