Could Spock have known of the success in retrieving the whales in The Voyage Home? Before going back to 1986?
Well here it is.
The HMS Bounty from the past (so the future ship), with the whales, was already in the present before Kirk and his crew began their journey to 1986.
Watch carefully, and if you time this , you will find that the "past" ship crashed in the San Francisco bay moments before the "present" crew started the sling shot around the sun. Start from the beginning and see how the scene cuts with Sarek just looking out at the bay. When we jump to the end of the film, we find ourselves reliving that moment, but moments after, Sarek spots the Bounty crashing into the Bay.
Spock is Spock, and would have seen the Bird of Pray on his sensors and would have registered 6 humans, a Vulcan and a pair the of humpback whales aboard that Klingon flea trap.
So, the entire movie as Spock and crew are meandering about San Francisco, he knew that they would find whales (although not how) and knew they would return, at least, to the future, but not knowing if it had worked in saving Earth.
Spock only knew that their mission was successful in bringing whales from the past to their present. However, he would still not know what steps were taken and circumstances surrounding the effort.