For most part you could sure, in fact a lot of 3D Prints come with printed parts. But for things like the hot end, motors, logic boards, power supply, screens, gears, belts, etc. Not really. At least not right now.

There is flexible filament you could use for belts, and some printers can print metal or metal infused plastic filament. But you would need such a level of precision that it just wouldn't make sense. Other firms of manufacturing is way cheaper, easier, and faster.

For the step motors, monitors, psu, and circuit boards. idt it'll ever be possible to print those. At least not in full, there a lot of tiny components, not to mention processors that are on the nanometer scale ( 0.000001mm ).

TLDR; You can/could print a lot of parts of a 3DP on a 3DP but I don't think you could ever print a whole 3DP. There's just to many parts that need to be very precise and aren't possible to print.