The question says it all.
Yes, in a somewhat round-about way. You can share the calendar with your firstname.lastname@example.org email address and give it permissions to manage the content. A discussion will be posted to the group's Discussion page (triggering any email notifications) with a link to the calendar. Anyone in the group that clicks the link to the calendar will be asked if they want to add it to their calendar. If you gave the group email permissions to manage the content, people will be able to do this once they've added it to their own calendar account.