From a user running conferences on Zulip:

One thing I noticed is that the process of inviting users is not as
streamlined as it could be. The typical scenario is that I past a list
of several hundred emails into the invite users list for the
organization
and it sends invite emails to all but a handful who already have Zulip
account with a different organization. I then have to manually add the
list of emails it didn't invite to the stream I want them to join. It
would be much better if it automatically added the users who already
have accounts to the streams I included in the invite (and send them
an email letting them know they have been added).

I don't think it'd be correct to automatically add the users to the invitation streams (that might very well not be one's intended resolution!), but I think offering a button that does so makes sense to me.