Да, вы можете вам нужно будет использовать Google Calendar API Google имеет ряд обучающих android
Простой пример Java найти на странице events.insert
// Initialize Calendar service with valid OAuth credentials
Calendar service = new Calendar.Builder(httpTransport, jsonFactory, credentials)
.setApplicationName("applicationName").build();
// Create and initialize a new event
Event event = new Event();
event.setSummary("Appointment");
event.setLocation("Somewhere");
ArrayList<EventAttendee> attendees = new ArrayList<EventAttendee>();
attendees.add(new EventAttendee().setEmail("attendeeEmail"));
// ...
event.setAttendees(attendees);
Date startDate = new Date();
Date endDate = new Date(startDate.getTime() + 3600000);
DateTime start = new DateTime(startDate, TimeZone.getTimeZone("UTC"));
event.setStart(new EventDateTime().setDateTime(start));
DateTime end = new DateTime(endDate, TimeZone.getTimeZone("UTC"));
event.setEnd(new EventDateTime().setDateTime(end));
// Insert the new event
Event createdEvent = service.events().insert('primary', event).execute();
Совет: использование calendar.list найти идентификатор календаря.
https://developers.google.com/google-apps/calendar/v3/reference/events/insert – DaImTo