Hello Michelle,
The service record for Patrick, assuming he is the 44 Leinster Regiment and 5910 Royal Irish Regiment, has survived and can be accessed on Ancestry in the "Pensions" records. I haven't had a chance to look at it, but by the date of entry on his medal index card, he was one of the original contingent.
I cannot see a service record for Gregory but the SWB card shows that he was with the 3rd (Reserve) Battalion on discharge. His enlistment date infers that he was a pre-war regular, but although he served overseas (and was awarded the British War and Victory Medals), he does not have the Star, so could not have gone overseas before the beginning of 1916, long after the 1st and 2nd Battalions did so. The actual medal rolls at Kew may shed more light on which battalion he served with.
Phil