At this time, Nimble does not have the ability to send calendar invites from within the application. However, when you add a contact to a Google Calendar event in Nimble, it will appear on their calendar. Your contact will not receive an invite/notification, but it will appear on their calendar.
If you would like to send an invite for an event to your contact, please do so through Google Calendar.
Events from your Google Calendars (that has been connected to Nimble in the Settings >> Networks & Imports page) will sync to Nimble and display in your Activities tab and on related contact records.