Is performing FUE on consecutive days (more than 2) better for yielding, healing, potential shock loss and graft survival?

There is no advantage of performing surgery over two or four consecutive days.  There is probably a disadvantage to you.  Most doctors perform surgery in one day.

There is no evidence that multi day procedures have any benefit over a single day session, as long as the grafts are extracted and placed within an 8 hour time frame.  If the clinic takes more than 8 hours to perform a 500 graft procedure, then you should probably look at a clinic that is more proficient in FUE.

There is no advantage to prolonging your procedure over 4 days. This most likely means that the FUE clinic or surgeon you are going to cannot perform more then 500 grafts in one day. Perhaps they are inexperienced at FUE. 

There is no advantage to spreading an FUE procedure over several days.  A particularly large FUE may be better done over two days, but four days for 2000 grafts is unnecessary. 

For 2000 grafts procedure, an experienced hair transplant surgeon should be able to do it in one day. There is no advantage to spread it to four days. 

a 4 day surgery means 4 anesthetic procedures, 4 days of your time and risks of graft dislodgment. A 2000 graft FUE should be done in a single session in the hands of an experienced hair surgeon