Earlier quoted context omitted.
For a good IMAP webmail client I recommend Rainloop: http://www.rainloop.net/
Yeah I use it in some places actually but unless I'm missing something, you can't connect to multiple accounts, see them simultaneously and get notifications on all of them.
If you do try it, please let us know of your feedback in the issue tracker! :)
(And that is, you can also run ownCloud with the Mail app locally. We’re working on improved caching.)