That would make sense, there always seems to be space down there when TP or EMT need to divert services (as in the recent incident on the Stockport viaduct). A Somewhere - Sheffield - Dore - Chinley - New Mills - Piccadilly would work well as a semi-fast, with the added benefit of giving New Mills a proper service (not the endless varieties of stoppers it currently gets).
Who knows what will come to pass, but a Piccadilly - Sheffield core service of 4 tph is supposed to happen when/if the Hope Valley Capacity Scheme is finally completed. The existing two fast (although fast is a generous description) services seem destined to remain, with the Liverpool - Norwich, split at Nottingham. The stopping service via New Mills is also to remain, with the hourly service supposed to serve all stations, rather than skipping quite a few as at present.
The residents around Chinley are most unhappy about losing their services to Stockport by TPE. The extra train might be fairly fast, but limited stop, X, Piccadilly, Stockport, Chinley, Hope, Dore & Totley, Sheffield, Y. That would give a central Hope Valley stop with quicker services for both commuters and leisure travellers to both Manchester and Sheffield - and Stockport.
New Mills Central has a half hourly service into Manchester on the Hope Valley. New Mills Newtown also gets 2 trains an hour on the Buxton line so residents in that area are well catered for by numbers of trains, albeit taking 30-40 minutes into Piccadilly on both lines.
However, details of new services and paths specifically down the Hope Valley are more a subject for the Hope Valley Capacity Scheme thread;
https://www.railforums.co.uk/threads/hope-valley-capacity-scheme.168285/