I had a testicle ultrasound twice and my penis wasn't covered for the actual exam.
First time it was a bit of an urgency and got examined by two female Docs. After a short interview I just lowered my undies and my willy might have been quite shrunken as it didn't seem to get in the way of the exam at all. They were discussing the finding as it went, which was quite interesting...
On a follow up visit, initially the nurse encouraged me to just get rid of the undies and hop on the table, but I let her cover me first with a little towel and then lowered the undies hehe. Then the Doc got rid of it and mid-exam she told me to hold my penis up, once it started to get in the way.
Both times there was no chance my stubby would stay flipped on my abdomen or under a towel ;-)