Can arcpy identify the MXD Label Expression Parser type?

[MicZatorsky_AEC]

In ArcMap (v10.8.1) MXDs, I can find label expressions easily with arcpy:

    if lyr.supports("LABELCLASSES"):
        log.debug("{} supports label classes:".format(lyr.name))
        for lblClass in lyr.labelClasses:
            log.debug("    Class Name {}".format(lblClass.className))
            log.debug("    Expression {}".format(lblClass.expression))

Is it possible to find the Parser type from the three that could be used?