Can I run Google Sketchup on an iPad? I use it a lot for work and I am interested in buying an iPad pro for this but I want to be able to run it without third party app.

Not unless they create iOS app version of it, its current requirements : http://help.sketchup.com/en/article/36208

There does not appear to be a version of Sketchup for iOS devices.

Google would need to make one for you to use it on an iPad.

It would appear no.

Google never made a Sketchup app for iOS.

There appears to be two Sketchup Viewer apps for viewing Sketchup files, though, but only to view and NOT edit.