Will my necrosis heal on its own? (Photos)

I am sorry to hear about the complication you have experienced.  The area of compromised tissue may “look worse, before it looks better”. 
In my opinion, the most important “factor” involved  with successful treatment of the complication will be close follow-up with your plastic surgeon (or seek to follow with another surgeon in your area).   He/she will be able to monitor for signs of infection and decide whether or not removal of unhealthy tissue and/or removal of exposed sutures is indicated.
 Yes, it is perfectly fine to leave the dry/dark tissue alone to "demarcate".  You will likely find that it will come off on its own and that you will likely have an open wound present. Dressing changes may be necessary for a period of time. The open wound  should go on to heal over the course of  several weeks,  hopefully without long-term sequelae.  However, sometimes, depending on the final appearance of the scar, scar revision surgery may be helpful. Also, concentrate on a well-balanced ( good protein source) diet  and avoid nicotine in all its forms.  Best wishes.

Thank you for your question. I am sorry for this complication. You need good local wound care and I believe it will heal by itself. Please follow instructions from your PS.