I've met a few examiners who would almost certainly take great offence at being asked. My IR examiner offered them willingly without prompting but I wouldn't have dared asked in case it put my test at risk. It's a terrifying prospect when you're already bunched about the test.
That said, my MEP examiner had in fact expired 7 days before my MEP skills test and the CAA were refusing to issue my IR on that basis and were suggesting I had to take both tests again.
This was of course resolved in a sensible way by the chief examiner but it goes to show that the examiners should be freely offering their licence as part of the briefing. I'm sure many do.