The short answer
No, as long as the background is pure white and you engrave normally. Laser software turns brightness into power: black gets full power, white gets none. A clean white background therefore stays untouched. The trouble starts with backgrounds that only look white. A photo's background is almost never pure white — shadows, paper texture and compression noise leave light grey pixels, and light grey still burns. On wood that shows up as a faint grey veil around the subject.
- Pure white background → can stay
- Almost white photo background → remove or clean it
- Transparent PNG → behaves like white