Will she? Or will she take the attitude that whatever it is, it is a law enforcement issue so some civilian carpenter can butt out?
Remember: at the point of divergence, it's the
exact same Murphy, with the
exact same attitudes. So yes, there may be some suspicion/distrust, just as she wasn't yet to the point of trusting Harry. Also remember: Murphy doesn't need to "call Michael for help" in order for Michael to show up via his own guidance.
But she'll be just as in-need of assistance from Michael as she was from Harry. How many times will Michael need to selflessly risk himself to pull her (and other SI) out of danger, before she trusts him ... at least a little bit?
Michael's fundamental goodness is something that will speak to Murphy; and his free and ready faith (which Harry *never* displays) will do so too.
= = =
In the end, of course, it will depend 100% on how Jim writes it; the whole point may be moot; maybe one or both of them die in the stories between GP & MM...