Hmmm... I think it will pay off if you start with embedded systems. Not least:
1. You will have a lot of material/tutorials regarding coding.
2. This will offer a more natural flow as most DSP programing material traditionally skip the basics.
3. By the time you take a DSP (after going through the embedded system development process) you will merely need just the architecture of the hardware and minimum material. Manuals will do in this case.
This is from my experience. Depending on your background you may just pursue your DSP course.