If one enters from the illegally operated Ports/Airports of the occupied by Turkey part of Cyprus then the answer is a big NO. If one enters from the legally operated Ports/Airports of the Republic...
It is because north Cyprus is illegally occupied by the Turkey and the Republic of Cyprus (non-occupied area) is a member of European Union. So officially the currency is Euro, but the occupied part...
It depends where are you in Cyprus. If you are in the capital city, max 30 minutes. If you are in the furthest point of North Cyprus it's about 2 hours, both by car.