Yes, it's possible to do that. Once in the Status tab, press on the three-dot icon in the upper-right corner and select "Status Privacy." From there, select either "My contacts except" to prevent certain people from seeing you've posted a status or "Only share with" so that only a select handful can view your status.
When that happens, a person who has not been cleared for viewing the status won't be able to see that you've posted a new WhatsApp status. None of the methods described in this article will pick up the hidden status if its owner decides to hide it from you.
Note: you need to change the privacy settings first, then upload the status. If you do it the other way around, it won't work.