Not trying to sell you snake oil, but..no...it's not the same. Cropping alters the composition. It is easier to create your composition when you can use the entire sensor and viewfinder compared to anticipating where you will crop for a cropped composition. And since (as others have mentioned) there are no FF cameras with the same pixel density as the highest MP crop sensors, you will have lower pixel density.
Perhaps it is time we stopped calling APS-C sensors "crop" sensors. They are just a different size sensor. Do we call FF sensors crop sensors as if they are cropped from medium format? Or medium format "cropped" since it is smaller than large format? There have always been many sizes for film and now digital sensors. When Kodak introduced the APS film cameras, nobody said, "Oh, that is just a cropped version of 35mm film." So, why is it that we began to call that particular sensor size "crop" in our digital age, when the sensor is the same (or similar) size as APS film? APS was an existing format - not something created when cameras went digital. (As an aside, the actual APS-C size is a cropped image, but not cropped from 35mm, but cropped from 30.2 × 16.7 mm, which was the maximum size of the film negative with an aspect ratio of 16:9).