This is sometimes called "bluebooking" as in those school blue book used for essays. I have done it before, and encourage my players to do so. It is very useful for adding flair and life to a character, as well as a personal life. I know that, both as a player and GM, I do not want to waste what little gaming time I have each week on any characters ongoing love life, child-rearing, or social time. Did that player win a local tournament in Tiger Woods' Urban Golf: Emerald City Edition*? I couldn't really care, as I have more important, and more inclusive things to do than play through that tourney. Knowing that another character won that tournament however, even if bluebooked? My character would either tease them about life priorities or ask for advice on playing, all good for role-playing fun.
Bluebooking is also good for handling all those Dependents.
I would not however, hand out any Karma, positive qualities or nuyen for it. I would, and have, added 1/1 contacts and negative qualities for bluebooking. New girlfriends are an obvious choice. As Farothel said, characters hooks as key here. Anything more is liable to start rebellion at the table. After all, karma is Karma, even if it is earmarked. That just means the character can spend their other Karma elsewhere. If the player chooses to spend their regular Karma on animal care to reflect the time spent at the shelter, reward them with uping the Loyalty rating of the contact at the shelter. Then give the character a job, perhaps saving those rare animals being served up at the Peaceable Kingdom restaurant, a job that the whole Crew will be needed for. That way everyone benefits from the player's extra effort.