I use Vaultwarden this way. When I login to the web interface (basically never) I get the following notice because I never verified my account's e-mail address:
> Verify your account's email address to unlock access to all features.
Also I am unable to change my account's e-mail address. That's the only "locked feature" I'm aware of. I also don't know of any other issues from not setting up SMTP.
edit: Oops, I thought you were ohCh6zos asking a clarifying question