Yes ~ it certainly does happen, but usually when the relationships are 'close' (sorry to say it, SR!).
I worked in an all-female environment, and within about a year we had all synchronised periods. We found it strange that at first we became irregular, and one by one we were all on at the same time!
The same thing has happened with me & my daughter. One month she was very late and eventually came on 2 weeks later..on the day I started :) we are still in sync much to Mr Pippas delight, LOL.