Will uninstalling sketch up pro and then re installing it erase my pro license
You don’t mention your operating system or method of uninstall so the answer is conditional.
On Windows, if you use Control Panel and uninstall SketchUp it will not remove the license so reinstalling you’ll still see the same license information and won’t need to re-authorize.
On OS X, if you simply delete the SketchUp 2014 folder from Applications and then reinstall then your license will remain.
On OS X, if you uninstall as detailed in our Knowledge Center then you will have to re-apply your license after reinstall.
Hope that helps!