It should be possible to convert logos and designs saved as PDF documents to DST Tajima embroidery format. However, we do not know any software that could do it directly, except for CorelDraw that supposedly has support for Tajima formats via some plugins and might be the only software that allows direct pdf to dst conversion.
Perhaps try to first convert or export the graphics from your .pdf file to some vector based format (.svg for example) and import it to embroidery software that has support for Tajima formats, which should make pdf to dst conversion much easier to achieve.