The chaps at Crofty wouldn't thank me for mentioning anything about access to their adit system. It is very secure indeed.
The "Barncoose Adit" starts "somewhere" down the valley and goes up under Blowinghouse, under Barncoose and to Druid's Shaft of Carn Brea. This is on the same lode as Dunkin's Shaft (pretty much) and I gather water was conveyed on Launders over stoping. I have a feeling that the Dolcoath deep adit somehow drains the workings, so water is about 30ft or so below the adit level "on that side". It would mean that theoretically, the adit level is above water level there. However, it will probably consist of half rotten timbers above flooded stopes.
There are some interesting documents on shaft capping "out the back" of Cornwall Studies Library and these document the removal and replacement of old concrete caps. I imagine yours is one of these. However, it may not be.
I know that Dolcoath deep adit is 30ft above the New Dolcoath Deep adit and people have been in both Dolcoath and Cooks Kitchen adits, which are on the same horizon as the Barncoose adit (in that area). Nobody has been in any workings that end, according to the people I've talked to.
I'm not sure if Highburrow East shaft pumped to surface, or not.... I think that's on something else on the plan.
Anyway, Crofty have made all of their adits and shafts very secure and there is no longer any access to any of it.