If you currently miss a week you won't get a weekly chest item and you be 1 item behind until the next patch's gear reset.
If anything under the new system missing out 1 week will be less impactful because multiple items lets you pick for a slot where your missing ilvl and get you back up to max ilvl in all slots faster then the current BfA weekly chest does.
Edit:Your acting like the chest is the only way to get gear during a given week....