If a user is not marked as Read-Only, what will happen when they connect to WebLink?
To add to Blake's response, accounts with named user licenses do not have to have to be read-only in order to log in to WebLink. Having a user license and the appropriate rights to the system should allow them to authenticate just as they would with Web Access or the desktop client. Once they log in they will be limited to read-only access because of the nature of WebLink, but that limitation doesn't need to be imposed on the named user's account.
Now, it is when you want to take advantage of retrieval licenses, to give a non-named user account the ability to access WebLink, that you need to configure the account for read-only access, as Blake noted.
This is taken from the WebLink Help Documentation:
"Reminder:When logging in through WebLink, you must specify a user account configured for read-only access for WebLink to properly use retrieval licenses. Similarly, the Public Portal Licensing and Web Distribution Portal Licensing features only take effect when logged in with a user account configured for read-only access."