I don't have any strong opinions about it, but I haven't seen any other application hold back on emails when I've seen them already in the UI (e.g., Twitter, LinkedIn, etc...).

It will be interesting to see if, the rare times this happens to most users, they'll actually intuitively understand that they didn't get an email because they saw it in the UI, versus think "Hey, I should have got an email about this notification that just happened but I didn't, maybe it's broken".