Yes. A designer can recreate an AI-generated logo as true vector artwork by redrawing its shapes and lettering in Adobe Illustrator instead of just enlarging the image. You keep your design; you gain a scalable file that stays sharp at any size.
Some AI logo tools produce a single raster image. Depending on how it was generated, that file may be too small to print, contain misspelled or melted text, have a background that won’t remove cleanly, or hide tiny artifacts that show up on a big banner. The idea is fine; the artwork just needs professional preparation.