Depends on the e-mail app/service you're using. If the account you are using syncs read status across devices, then yes, eventually (once the account is synced), the notification will go away.
For instance, on GMail, the sync is from instantaneous to a couple minutes (don't know why it varies, but some users report that it takes a while for the notification to go away on theirs... on mine it's always only a few seconds apart). On my Exchange account, however, although it is set to sync on 'Push', it always takes a while for the sync to happen when I delete or read a message on my desktop...but it eventually does happen.
10-01-2017 09:08 PM