Depends what you mean “work”.
Would it be possible? Maybe - if you could find the Paths and suitable rolling stock.
Would it be viable? Maybe - if you charged around £100 a ticket and could be sure of finding enough passengers (100+ for each train) prepared to spend that + extra for any refreshments for a 3h30 to 4h journey each way to the Yorkshire Dales.
But I’d be surprised if you Could find that many people.
I've tried to create a Timetable which is somewhat plausible. You would probably get Class 769's as they are being converted over from their diesel variants the 319's. Have 2+2 and hopefully some comfortable seats maybe with the faux leather for easy cleaning of Mud off the seats.
BHM - SOT (46 Mins) Based on UID C72044, identity 1H09, TSC 22180014, headcode 3007 (Quicker under wires)
SOT - CRE (< 21 Mins) Based on UID C77110, identity 1K55, TSC 22277000, headcode 5155 (Quicker under wires and skipping Kidsgrove, Alsager)
CRE - SPT (< 28 Mins) Based on UID L07452, identity 1W10, TSC 25434000 (Quicker under wires and skipping Wilmslow)
SPT (5 Mins to split)
To Carlisle
SPT - DGT (< 20 Mins) Based on UID C85684, identity 1B63, TSC 11817020, headcode 6009 (Quicker under wires and skipping Deansgate and Oxford Road)
DGT - BON (< 14 Mins) Based on UID Y41332, identity 1N52, TSC 12362822, headcode 9300 (Skipping Deansgate and Salford Cresent)
BON - BBN (< 29 Mins) Based on UID C88787, identity 2B89, TSC 12242110, headcode 9598 (Skipping Hall i' th' Wood, Bromley Cross and Darwen)
BBN - CLH (< 23 Mins) Based on UID Y43182, identity 2N59, TSC 12349820, headcode 9596 (Skipping Ramsgreave & Wilpshire, Langho and Whalley)
CLH - SET (Literally no train goes this way anymore) Line Speed appears to be 30 and similar distance as Clitheroe to Blackburn so around 20 minutes maybe?
SET - CAR (< 1 Hour 39 Mins) Based on UID C90656, identity 2H10, TSC 21151900, headcode 5600 (Skipping Appleby, Langwathby, Lanzonby & Kirkoswald and Armathwaite)
Journey Time of around 5 Hours (I would guess some savings so time to Settle is 3 Hours 21 Minutes. Reach Settle at 10:00, 11:00 and 12:00 so leave at 06:30, 07:30 and 08:30
To Sheffield
SPT - MAN (8 Mins) Based on UID Y43643, identity 2S91, TSC 12226820, headcode 6174
MAN (5 Mins to reverse)
MAN - SHF (Around 1 Hour 20 Mins) Based on UID C77200, identity 1R50, TSC 22269000, headcode 9250 (Opposite direction and taking the Hope Valley Line section from Manchester Piccadilly to Chinley not the Manchester-Crewe Line and the Buxton Line)
Journey Time of Somewhere in the Region of 3 Hours 13 Minutes. Time to Chinley of around 2 Hours 45 Minutes. Leaving with the other side leaving at 06:30, 07:30 and 08:30 you arrive in Chinley at 09:15, 10:15 and 11:15
I've added UID's where I have based the speed off an existing service but I have also added extra info for skipped stops or where Electric Traction can be used while the one I have found is pathed as Diesel only.
Run them Easter Holiday, then on Weekends until Spring Bank, and after then each day until the end of the season (September).