They sell multiple Google connectors, which one are you referring to?
I've worked with a few of them,
Works really well and everything that is exposed through the API you also gain access to.
Keep in mind that GA wont track single visitors so you only gain access to a aggregated data set which will require some data modelling to get all dimensions and metrics to line up nicely. The quick start template will get you started pretty quickly. If you are running a very large GA implementation with 200+ sites (not pages) make sure you do proper planning and set up a good incremental reload since the reload times will be massive other wise.
Simple. Very simple. Connect, extract data and your done. New version also leverages oAuth (I think) which gives you a boost in security.
Personal opinions - Not associated with QT.
Spot on Alexander - and yes the Google Spreadsheet Connector V2 uses oAuth and we are deprecating/removing V1 of this Connector.
Joe, also not sure which specific connectors you might be referring to as we do have connectors to a number of Google APIs. Feel free to provide more detail here or DM me.