It'd be a little strange, but its really not any worse than adding a day in February every four years.
If you tried then those who observe religious days will keep their cycle, and will not go to work on the real weekend (even those who otherwise wouldn't care would make a point about it), which will be out of sync with the new calendar weekend. It won't take many people doing that for the calendar to fail to be accepted.
What I can't figure out is what algorithm they use to calculate when to add an extra week. It seems slightly irregular, but I asssume there must be a simple formula I could use in a date library to account for it.