This is absolutely fine to apply for correction of COPR original date of entry. However keep in your mind that when you apply for citizenship, this original date of entry is useless since you may left canada a week after you original date on entry and came back later. The key point is the proof of documents that you have including study permit, work permit, old passport visas and even the translation of your passport pages which shows when you have been away from canada and when did you come back (e.g, during the vacation or visiting back home).