Unlike some free editors that insert periodic "chirps" or voiceovers, DaVinci Resolve free does not add any audio watermarks to your final mix.
However, one question plagues almost every beginner before they hit that download button:
The only time you will see a DaVinci Resolve watermark is if you use a feature exclusive to the paid . The software will typically show a warning before you apply these, and a large overlay will appear in the preview window and final export if they remain in your project.