Does an image edited and saved/exported with 1200x800 pixels at 300 ppi look any different online than the same image saved/exported with 1200x800 pixels at 72 ppi?
No.
A bitmap produced either on-screen or on paper from the image will be identical.
The only difference would be the default print size from some applications, and only then if the image size is not specified in any other way.
If you were to open the image in a simple image viewer (something akin to MS Paint that handles images, but not page layout, such as Adobe Illustrator) and press Print, you may find it sets the default print size based on the resolution, so the 300 PPI print would be 6x4" while the 72 PPI print would be 17x11"... assuming it didn't just auto-fit to the default paper size.
The only way to stop someone printing it at higher than 72 PPI on a 6x4" photo would be to only upload the image at 432x288 resolution.