I will answer the last part first. Yes you can add your nomination certificate to your express entry profile depending on which stream you were nominated in. The certificate will say whether or not it can be added to express entry. For the first part, When you are a permanent resident and you received your PR card in the mail you do not need any Canadian visa to travel. In fact all of your temporary resident visas would become invalid once they issued the COPR. So if you are in canada and get the COPR, you will need to wait for the PR card before you can travel outside. The only difference is when you apply through an Embassy in your home country. If the Embassy processes your COPR, they will automatically issue a one-time PR visa for you to land in Canada.