I have one google account for my android phone. Now I set up a work email at gmail to use the shared calendar and keep things separated. For convenience I downloaded the google calendar app to display events from the calendar on my phone. I followed the steps to add another google account to my phone via Settings -> Accounts -> Add Account -> Google. Everything worked out fine, but on the google calender no events are shown. When I go to Settings -> Accounts -> Google -> workaccount I can't see the toggle for Calendar syncing. In the phone account I see this though.
With the same account I added the calendar to thunderbird using lightning and followed the procedure which worked out fine. Therefore I assume that the accounts calendar is visible.
My phone is a Oneplus One running CM 12.1 (Android 5.11)