If Email Type is HTML, no date is included in the content of the notification email (regardless of events):

If Email Type is Text, date is included in the content of the notification email for issuecommentedited but not issuecommented or issueupdated:

What's worth noticing is the included date has a different format as the one specified in Look and Feel:

This causes confusion/inconvenience to customers. Though the templates can be edited but this practice is complex and unsupported. Customers prefer this date format to resemble the Look and Feel format or at least to be given an option for configuring it easily.