The conductor will definitely care, and the likelihood is that you would be forced to pay a new ticket for that journey (which on the day, from Sheffield to London St. Pancras you're probably looking at £70-£100). In the worst case scenario, you'll also be given a penalty fare.
Having checked the East Midlands Train website, Sheffield is classed as a 'penalty fare station', so you would be required to pay the penalty fare, which for East Midlands Trains, is defined as:
"The Penalty Fare is £20 or double the single Anytime fare to the next station stop – whichever is the greater amount."
Things to note:
- You can't make changes to the journey on-board the train. Therefore if you wish to change the time of your Advance Ticket then you'd need to do so before your first journey.
- If you do change the time of your ticket, you'll be liable to pay any difference between the cost of your original Advance Ticket and the new ticket that you are purchasing (the route cannot be changed). There is also a £10 admin fee per ticket change.
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TL;DR - Don't risk it.