No, it would not be accepted. The 7 day cycle is strict - you can not add or remove days from it. It might be fine for work, but it will not be fine for religious observance.
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.