The short answer - NO.
In 2016 the Michigan legislature passed Senate Bill 992. Here is the full version. In a nutshell, the law prohibits municipalities from regulating unmanned aircraft systems. It provides, "Except as expressly authorized by statute, a political subdivision shall not enact or enforce an ordinance or resolution that regulates the ownership or operation of unmanned aircraft or otherwise engage in the regulation of the ownership or operation of unmanned aircraft." So no, cities may not enact their own rules.
Of course, federal rules still apply. Just because a city does not regulate drone use does not mean that anything goes. SB 992 also provides, "This act does not affect federal preemption of state law." Thus, FAA rules remain in effect at all times everywhere.