Yes. A designer can recreate an AI-generated logo as true vector artwork by redrawing its shapes and lettering in Adobe Illustrator, rather than simply enlarging the image. The result keeps your design but becomes a scalable file that stays sharp at any size.
Some AI logo tools produce a single raster image (PNG or JPG). Depending on how it was generated, that file may be too small for print, contain misspelled or warped text, have a background that will not remove cleanly, or include tiny artifacts that show up on a large banner. None of that means the idea is bad; it means the artwork needs professional preparation before production.