No. No they don’t.
Here’s some samples from today’s data from Tennessee.
In all of the cases there is no noticeable change in the growth rate of the virus after the mask mandate went into affect. If anything the numbers grew faster indicating that the course of the virus is generally unchanged with or without the mandate in place.
And here’s an outlier:
In Hamblen County, the mask mandate actually went into place after the active case count had organically dropped by itself.