I realise that a definitive answer would be challenging but I am looking for pointers/input/suggestions.
The scenario is as you see it in the extract of the remarks column of the medal roll below. Can one assume that, if the man is attached to Pilcher/Broadwood as per the remarks, he would have been with these gentlemen where they were in their campaigning in the Cape Colony and Orange Free State?
I want to write this man's summary and want to be as accurate as possible.
For what it is worth, the following is how I would approach things. First, I would look in the "Services of Boer War Officers" (Savannah publications) for your man and see if any periods of territorial-specific duty are shown. They sometimes are. If so, I would try and mesh those periods in with the bio's of Brig/Gen. Broadwood and Col. Pilcher. If that cannot be done, then generalities might have to be used. There are many references to both Broadwood and Pilcher in Amery, Maurice and Creswicke. For example, Creswicke Vol.7 [age xi) shows the components of Col. Pilcher's column in the Central ORC during Midsummer of 1901. Brig.Gen Broadwood's column on a later page is shown in the Northern ORC. There may well be more in other references.
ADC was an officer (at least a Captain) on the personal staff of a senior officer. Was your man an officer with the ASC? Again, "Services of Officers" should tell you one way or the other. It might be worthwhile to research out the structure of columns in the later period of the campaign. For example, did they routinely have an ASC detachment - or were they reliant for resupply from depots? If the latter, your man would have a fair bit of co-ordination to do. He was probably worked off his feet, anyway.
Anyway, that is the path I would follow. These are just suggestions.
IL's suggestions offer a good way forward. I think it is difficult in these situation to know for how long there were attached to the columns. The fact that they mention service with these men may mean it was not a full-time appointment but it could also imply that he was attached from a different unit that did not ordinarily comprise the column (which were somewhat fluid anyway).
As you will know, the KSA roll can be helpful here as they often work out the eligibility by listing service dates on the roll.
You could search the shipping records to see if his movements are listed but only if he is an officer.
The man in question is Arnold Herklots - I have his DSO group. His QSA is to the ASC and we know from the LG that he was appointed to the ASC in September 1902 having served through the war seconded to the Imperial Yeomanry as a Lieutenant.
It would have been in this capacity that he was with Pilcher/Broadwood and their columns in the CC and OFS.
What I have done is trawl through the The Times History of the War and, using Pilcher as a search, tracked his column's movements through the CC and OFS - he saw quite a bit of action and, unless someone convinces me to the contrary, I am drawing the conclusion that Herklots as an attached 2nd Lieutenant, was with him until Herklots left for the Transvaal - it would be impossible to determine if he was with them all of the time.
I sadly don't have "Services of Boer War Officers" IL I wish I did!