What you describe sounds like you need a transactional email service. This has a reasonably straightforard desciption of transactional vs marketing emails. MailChimp offers transaction email sending for paid accounts (formerly separate called Mandrill).
The one big red flag that I would look out for is the amount of spam flags these emails might generate. If you allow any of your users to send an email whenever they want, that can be abused pretty easily. And if you send enough bad emails that get flagged as spam by end users, MailChimp (and any mail sending service) will disable your account.
My first inclination would be to allow internal messaging on your site, and to send a daily summary out to members. That way you can keep some control over how many emails you send out and (to some extent) the content in those emails.
But every case will be different and depending on the size of your community and their relationships this might not be necessary.