of course not.. if you have bad design in lead screws, or x axis carriage design , z wobble etc will always rear its ugly head.
However, assuming the build is solid, the design of it is good, and everything is tight and precise, auto bed leveling will mitigate the next biggest issue faced by 3d printers. Layer #1.
If layer 1 is off, the rest of the print may as well be scrapped. Not always, but a great first layer sets itself up for the rest of the print.