No Rick, it will not stop. The jacks are DOWN. The only way to stop it is to disconnect the buzzer lead in some manner, or turn the ignition off. It is a safety feature.
Wannabe, you are absolutely correct in running the engine while putting the jacks down and extending the slides, or retracting the slides and then retracting the jacks on the Winnebago chassis. I believe that is for all the DP's in the Winni line, and a recommended procedure.
You could find the line to the beeper and unplug it, or, as you stated tape it or tape a sponge around it so the sound is muffled.
Good luck. I know how frustrating it can be having that beeper blaring at you. In my case it was 80-100 miles down the road and it would shut off sometime, but it was with the Jacks up. I just ignore it when the jacks are down as it is less than a couple minutes. Besides, I can operate the jacks from the outside and never hear the alarm until I go in to extend the slides and that is less than a minute. However, if your ears are that sensitive, I do understand.
As for DW, when we stop she's out the door with the pooch and doesn't come back in until the slides are extended. Then we swap places, me out, her setting up inside.
Happy trails.
Edited: I believe in your particular case you would not want to interrupt the power lead to the key pad. That would disable everything and you would not be able to extend the jacks, unless you could put up with the few minutes and then turn it of. It may be a better solution, for you, to just interrupt the alarm bell, or muffle it. JMHO
Good luck.