I would look on the manufacturer's website... if they don't say no, then shit hits the fan, you can say well according to the manufacturer's instructions, flipping it upside down is irrelevant and put the liability onto them.
I understand the need for an organized patient, especially in CCT in ICU's...but if it's just for a short trip down the road, it shouldn't be as big of a deal. I have seen ICU nurses flip out on people for moving a line out of place but that is a critical environment where that nurse needs to know exactly where everything is.
**EDIT TO ADD** I have seen this done in the OR before so the wires are leading out of the surgical field.