We have aws and azure, so google-cloud-platform would certainly seem to belong, as they are the other big public cloud option. Plus, we do already have the more specific tags about specific parts of their cloud.
As to its purpose, I'd say it should be used like the AWS and Azure tags. To tag questions about syaydmin-y things specific to Google's cloud platform, the same way the Azure and AWS tags are [supposed to be] used.
However Google support wants to handle that is their business. If they want to steer sysyadmin-y questions about their cloud our way, and answer them, I can't say I have any real feelings either way. On the one hand, I dislike the site being used as a substitute for actual product support, but on the other, the big public cloud providers are relevant to systems administration in today's world.
That said, if a bunch of window-licking morons ask moronic, window-licky questions about Google's cloud, they'll get the same reception that all the other crappy questions get around here - lots of downvotes and/or closed, regardless of whether or not that hurts people's feelings or makes them think of us as mean and unwelcoming. (The off-topic close reason that means approximately "you didn't give us enough information" seems like a relevant thing to mention at this point.)