Like antibiotic resistance bacteria, if you continue to flood the internet with begging, people will become completely immune to those types of requests (no matter what the cause or how worthy they might be).
This could happen here also. Creating a familiarity. So even if a person is initially irritated, after a month when he / she goes to make a donation, it would be to a charity that is familiar than a completely unknown one.
But buying SEO juice with unused domains the same way spammers do is probably a better idea - then a google search is going to turn up the correct sites.
Is there research to confirm this?
It could be that people's willingness to respond to "internet begging" doesn't tend to zero but rather a nonzero constant as they encounter more of it. In that case you'd be better off with more websites that do it.