Prologue: The Crossing shows us what happened right after Prometheus and expands a little on the Engineers and David. Having watched it AFTER Covenant the other day, I strongly believe it should have been made a part of it, not a separate online release. You'll understand why after you see Covenant for yourself.
If you're an Alien fan then this little short will add more cohesion and structure to the narrative so definitely watch it BEFORE seeing Covenant, as well as Prologue: Last Supper. Also, check out this Alien/Predator time-line to better understand the order of events in what seems to start looking like a little big mess: http://www.imdb.com/list/ls003104998/
If you're an Alien fan then this little short will add more cohesion and structure to the narrative so definitely watch it BEFORE seeing Covenant, as well as Prologue: Last Supper. Also, check out this Alien/Predator time-line to better understand the order of events in what seems to start looking like a little big mess: http://www.imdb.com/list/ls003104998/