Yes, she would
This isn't explicitly laid out in the rules, but it can be inferred.
In addition, each class has a number of favored skills, called class
skills. It is easier for your character to become more proficient in
these skills, as they represent part of his professional training and
constant practice. You gain a +3 bonus on all class skills that you
put ranks into.
Pathfinder doesn't force you to keep track of which ranks you got from which class, just the number you're getting per level. So, yes, that means that if you multiclass, all skills from both classes are considered class skills regardless of which class you're leveling at the time.
Consider the class skills part of your character's portfolio. Since your example Fighter above decided she'd learn the ways of being a Cleric, doesn't mean that during the process she's stopped being a Fighter, and as such could have been working on improving her survival (something her Fighter training has made her predisposed to) during the time learning how to be a Cleric.