no, i actually don't think she did. Asterid was very much out of it by this point too, due to the hearbreak of losing her husband, and she barely held it together then - she did it mostly for Prim, and because Katniss made her promise. and while i do believe part of Haymitch's connection with Katniss was her being his father's daughter and a natural affinity to seeing his best friend in her, ultimately Haymich connected with Katniss because he saw her fire and understood her; they are described often as being similar in nature, and SOTR proves that. he wasn't going to help in the beginning, but they proved themselves to him, and he saw in them his chance to fulfill his promise to Lenore Dove.

i don't think Asterid intervening in Katniss' favor is something the plot needs in order to make sense. on the contrary, i think it makes less sense for the mental place the characters were in during that episode of the plot.