QuickBooks does not add any data to your books to 'close' them. It does not even have a closing process.
It does shift current earnings to retained earnings on your balance sheet using your fiscal year setting, but that's all and it's only at report time.
So, you can continue to work on last year without issue.
The closing date has nothing to do with how reports work. It's just a date that prompts for the closing password if you try to edit transactions before that date. Resetting the date or removing it does not change the data file in any other way.