I’ve just had a run through to check, and while the password is not required on the sign-up, if you leave it blank the email you get sent asks you to set one before you can log in/activate:
Though @pfaffman is right, you can indeed ignore that too, and go straight to log in and select “Skip the password; email me a login link” and you get a log-in link without the need to set a password. 
I suppose the key bit is that you follow a link from an email to verify your email address (activation, set password, log in link), and how you access the account afterwards is up to you.