In eDrawings, go into the Options, there is an option to use the license server or not. You will be running the free version of eDrawings if you toggle that setting off.
So yes you can install eDrawings on other computers and not pull a Pro license from the SNL.
Your're also in luck that the ability to measure an e-Drawing is determined by the maker of the e-Drawing, not by the viewer. Only a professional license can make e-Drawings measurable, but any license can measure them once they are produced.