Will my coiled mousepad get permanent creases?

Yes, and if it’s been coiled for weeks or months, the rubber backing “takes a set” that may be impossible to fully remove. Rolling it opposite for a few days helps a little, but heat (hair dryer on low, then flat under books) works better—though some creases remain if coiled tight for years. Prevention is the only reliable fix: store flat or roll loosely with fabric side out.