Yes, but the fact that AwardWallet displays all stored passwords in plain text is a major system weakness. There is no reason to do this.
If the passwords were not displayed in plain text then a hack on AwardWallet accounts would not allow access to the account username/passwords of all accounts tracked within (except if the password for those is the same).
Sure it would - you'd just login in to AW, and have it log in to the loyalty account. To do that, you just click on the name of the travel company.