Roundup should also work well as a user helpdesk
application.
Therefor it competes with request tracker. You should
take a look
at request tracker which work quite well.

My suggestion is to add a scheme which will allow requests
to be made by anonymous users, but record the email
addresses
as requestors. Thus it should be recorded when a mail
gets send to the 
requestor email addess.

Additionally it would be good if normal email addresses
could be added to the nosy list and kept. So the
requestor or "client" property would be use the same
Class as the nosy list which can hold a list of users
or email addesses.

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I believe that the "anonymous" users you want to have can be handled  
right now by having automatic registration of unknown users in the  
mail gateway, but having their initial Role be set to something with  
almost no Permissions. Then all the current mechanisms work just  
fine, including the sender identification and nosy lists.  
 
Please indicate whether this is reasonable or not - I probably won't 
have time to evaluate "request tracker" for some time. 
 

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This is hard to tell without actually having a working setup
which tries to do this. It might be reasonable, but it would
also assume that this list of "ExternalUser" is hidden at
the right places and does not have to deal with their own
details. 

However I think that request tracker really has a good
concept in this regard
as a requestor only gets mail on certain occasions, but the
bugtracker helps several people to organise these responses.

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"External User" is the way to approach it, yes.