Flying Considerations during an Eclipse?
Do Pilots flying during this time need to be Night Current?


No, that time does not fall within what the FAA considers "night" 

The FAA defines night currency in FAA FAR 61.57 


  FAA FAR 61.57
  
  (b) Night takeoff and landing experience. (1) Except as provided in
  paragraph (e) of this section, no person may act as pilot in command
  of an aircraft carrying passengers during the period beginning 1
  hour after sunset and ending 1 hour before sunrise, unless within
  the preceding 90 days that person has made at least three takeoffs and
  three landings to a full stop during the period beginning 1 hour after
  sunset and ending 1 hour before sunrise, and—





  Can time logged during the eclipse be logged as Night Conditions?


Nope, same reason as above it does not fall in what the FAA considers "night".