Yes they do check those. Almost every trip I see security checking cars. They are more rigid at the Poly about parking limits at the moment because the construction has closed the smaller lot in front of Rapa Nui. That's putting more pressure on the main lot. So it would be good to make the pass visible.
You should ask the Poly about using the cover though I cannot see why it would be a problem. However, unlike what was suggested you cannot call the front desk. All calls, even those made from a room phone at the resort, are routed through the call centres. They will answer as though they are the Poly but it will be the call centre. So, I'd be sure to ask the front desk when I check in rather than trusting a call centre CM.