Since most modern digital displays do support 480p mode, won’t they “re-scale” that resolution mode anyway to fit the screen (either by aspect ratio with black borders OR full screen stretch)?
A modern display will re-scale anything other than a signal sent at its native resolution.
If so, doesn’t that add as much lag as it would with 240p upscaling if supported by the display?
No, scaling adds relatively little lag (usually none). It’s picture processing and especially deinterlacing that adds the most lag. Especially in the case of 240p which is nearly always recognised incorrectly as 480i.