No, this will not do it. Any user coming from an HTTP connection will appear very briefly on the Dovecot server and is unlikely to appear on the "doveadm who" list. This is a result of the HTTP connectionless protocol, nothing to do with Dovecot (ie connects-carries a brief data transmission/commands-disconnects-connects again after a predetermined time). The connection time is very brief, even though you can probably catch a few if you insist on typing doveadm who.

If like from Nick Edwards suggested a imapproxy is used it will. imapproxy is keeping the connection open. doveadm who will give you a list of all actual logged in users. Without imapproxy you are right: Every page reload will cause a login and a logoff. I get some webmail users by "accident". To get an overview how many users used roudcube within a period check the database table users/last_login.

Andreas