Deploying an anchor while on a mooring seems like a receipt for disaster. I would only consider deploying an anchor while attached to a mooring if I thought the mooring was inadequate for my boat
and conditions. Of course, if I thought this, I wouldn’t be on that mooring.
I suppose I could conceive of a scenario that would force me to be on a poor mooring, but then we’re into dealing with bad situations. At which point I’d do whatever I needed to do. To deploy an anchor I probably launch it from my dinghy
. Or if I could manage it, I’d set the anchor first and arrange it so I could back down and then pick up the mooring.
But seriously, none of these options are good. Much better to be swinging from your own good anchor and rode (assuming you have good anchor and rode) than playing with what you suggest.