Chrome books can easily remote into PC desktops from anywhere so long as you are logged into chrome with the same account on your chrome book and PC, for the PC client you will need to install Chrome Remote Desktop extention, once you do you have to start it up from the Chrome Web Browser.
It should look like this. Then all you have to do is setup the required 6 number pin. Then go on to your chrome book and start up the chrome remote desktop app, and you should see your computer. Then it is a matter of typing in your pin.
If you are planning on playing games through it well you might run into some problems, which is much to be expected with any remote desktop app. First you most games will not work in fullscreen, second you will not be able to play lag free. So games like Caster as shown in the image really isn't playable.