Absolutely. I have it installed on my phone, tablet, and Apple TV. It does not however support multiple accounts logged in at the same time.
You can configure each device and its notifications so, say you want to get immediate notifications on your phone, you can, but your tablet you dont want any, just turn them off. There are options in the Nest app as well as the OS of your device to turn on and off notifications to give you more control.
I am also my parents IT person. So when I add devices to their house, I just setup their devices using my account and name their cameras as theirs so I can track them. They can then also have it on their phone or tablet as well using the same login to Nest but will see all of your cams, thermostats and protects as well.