The Pixel uses as much data as you want it to. If you want to restrict data for certain apps, you can do that. If you're on a quality mobile network, be aware that some apps like Facebook, YouTube, etc will see that you have a good connection so (for example) YouTube will serve you up super high quality video so that's going to use more data. This isn't anything to do with the phone.
I have never turned off my data on any Android phone that I've used. I use WiFi at work and home. I get a full day easy with my 2016 Pixel XL. I'm not always on it, playing heavy battery sucking games, but the data connection does not drain the battery at all.
Unless you're on a very small (< 500MB) data plan, you'll be fine. Even then, you can set your data limit in the settings to warn you then shut off your data so you don't get robbed by your carrier. I think you'll love your Pixel 2.