You don't use your eyes to drink from a cup of coffee, unless it's to check how much coffee is in the cup. Eyes are not required for proprioception.
My experiments using straws in VR just led me to stabbing myself in the gum, lip, nose and cheek in various painful ways. The perfect vessel is a long neck beer bottle. Easy to get into your face-hole and won't bang against your goggles. The downside is how easy it is to knock over.
No, but they will mess with and override proprioception. I've used the Vision Pro and the first time you try to take a drink with it you'll probably miss your mouth. I think the main reason is that you see the cup coming towards your slightly offset "eyes" and your body automatically adjusts to match.
I think if I had closed my eyes (I didn't try that) I would have done better.