Definitely not in the core, and no addon that I'm aware of. I used to think I'd like this feature, especially for those who don't have access to the site due to proxies or firewalls, but still have access to email. But the more I thought about it, the more I think designing such an addon that works well would be an absolute nightmare to code and still maintain a secure site. Not to mention, I could just see a spammer sneaking through and then mail bombing your forums with spam.
A Helpdesk works actually this way the only big difference is that a helpdesk makes a private threads instead of a public ones, why not applying the same principle for a forum?
I find it restrictive to have to jump to the web-forum everytime I want to answer a post which answers arrived to me by email, the natural thing would be to simply replay that email (as in a helpdesk), don't you think so?
Google Groups also features the answer by email feature. They resolve the security issue in the way that only registered and allowed users are able to post by email and you are even able to moderate every single email (we use this feature in our School as we use Google Groups and are able to moderate students replay by email).
I understand the security thing, but could it be resolved my saying who can and who can't post by email?
(BTW. IPB has an Helpdesk Module integrated in their IP.Nexus but I don't know why they do not use the forum module in it, which is strange thing actually.)
Wordpress also suggests that you use a very obscure email, and doesn't verify who's sending it. There's also a lot more that goes into setting it up, with permissions, where to post, who to post as, etc. that makes it hard to accomplish & manage from a coding stand point.
Not exactly what you're you're looking for, but I have a PHP class that will generate an RSS feed from an email inbox. The RSS feed can be fed into XenForo as posts.
I wanted a way to get Google Alerts as an RSS feed, and of course I decided I wanted this just a couple weeks after Google dropped RSS delivery of alerts.
It's based on the mail2rss class at phpclasses.org, modifield to process HTML emails (original version just ignores the HTML), and tweaked to massage the Google Alerts closer to what I want for posting. Tweaks are still in process but at this point it works with XenForo.
It's astonishing that more and more years go by and no forum developer wants to grab the Yahoo e-mail list customer base. It's millions of users strong and showing no sign of going away. New Yahoo lists are started all the time.
@erich37 Thanks for posting that link. I expressed why supporting post-by-email and thus migration of Yahoo Groups communities over to XenForo would be a huge win for not a lot of programming effort.
Also, the e-mail detection doesn't have to be perfect. These yahoo groups folks are used to things being clunky and not always working properly. They're used to conversations not being nested properly. They have very low expectations. So the idea that XenForo cannot support such a feature unless it's "bulletproof" shows a lack of understanding of the audience.
Also, some code was posted that will allow Watched Threads to continue to produce alerts and email notifications, even if the watched thread remains unread by the watching member. This produces part of the functionality, by allowing users to receive email copies of posts from threads they are subscribed to.