At the moment a μ will not match \mu. As the display routines already turn the latter into the former when necessary, it is probably best to auto-convert all unicode symbols with a TeX equivalent to their TeX equivalents on input.
This was added a while ago in a patch by Connor 8c98d09cf11 and now works as expected: input of greek characters as unicode will convert them and internally store them as TeX equivalents.
At the moment a
μ
will not match\mu
. As the display routines already turn the latter into the former when necessary, it is probably best to auto-convert all unicode symbols with a TeX equivalent to their TeX equivalents on input.