Your wallet will continuously backup, even if you never open Exodus. This is because your funds live on the blockchain and Exodus is a blockchain interface that reflects the data found there.
As long as you keep your 12-word secret phrase safe, you will be able to restore access to your wallet at any time.
When you restore your wallet from the 12 words, FEX overwrites any previously existing FEX wallet on your system and re-generates the private keys for the wallet using those 12 words as the seed. Because the secret 12-word phrase is not connected to any password, that means that after restoring, there is no password protection on your wallet. It must be re-enabled by setting up a new one in the Backup menu. After restoring from your secret 12-word phrase, the first thing your should do is protect your wallet with a password.
Leaving your wallet unencrypted leaves you open to easy theft, so it is important you go through the backup process again. Remember to set a unique password, that you don’t use in other services. Re-using passwords opens you up to the risk of theft.