Well, it works, eventually!
My first goof was to put an apostrophe in the title of the calendar within the component - this will NOT work with apostrophes in the calendar name!
Once I'd found the right HTML (Google Calendar was having a slow moment, so I had to figure it out manually), and put it all in I eventually got the calendar showing up.
A limitation of Google Calendar (not the component) is that it will only show a month's events in agenda view by default - a pain if you are trying to show school term dates for example - you want everything showing up!
Clicking an event in this opens a new window to give you more info, direct inside Google Calendar - a bit clunky IMHO.
I ended up resorting to using this component, linking on the menu to a blank static content item, and publishing the upcoming GCalendar events module in the inset position. The problem with the module is horrible date formatting (and an overly techy process of changing it), and the date being on a separate line form the event name (might look OK when I have some more events in there though).
Overall, it works, but don't expect to have it perfect in 5 minutes!