Anon monk can be used by someone who--for whatever reason--wants to get a feel for the monastery before creating a login. Whether that person concludes that this is a nice place and creates a (character? account?) or goes away will depend on what s/he thinks of the monastery; her/his impressions of the monastery will come from the only available source: personal experiences as an anon monk.

Of course some people will only show up when they have questions they want answers to, but the same is true for some named people. If it is clear that the person only comes here to use us as a helpdesk ("email me because I can't check here" is a giveaway), then, if the question is very specific to the person, I probably won't answer it. If the person participates in the monastery (and I don't consider participation or lack of it to be in the moniker) or doesn't participate but the question will be of interest to others, I see no reason not to treat it as I would any other 'good' question.