Yes and No! If they used a dilution factor... in their previous analysis and the final results are in ppm or ug/g, then no. If the sample is expressed as ug/mL from AAS or chromatography and does not include the sample weight, extraction volume, dilution factor..., then yes.
I should be more precise in my answer! ppm (parts per million) and ppb (parts per billion) are a 'generic' term used by the public and not the analyst. There is even ppt, and ppq. Thus, ppm can refer to ug/g, ug/mL, or even ug/cm3 (used for gases).
When doing the calculations described above, a critical factor in soil science is soil moisture. Are the ppm values you needed to convert based on dry soil weight of soil at a set water holding capacity? Residue levels can be reported either way, but most commonly they are based on dry soil weight which can be considerably higher than for "moist soils".