Hi TD-Max,
With a quilted cover … generally no. Post #2 here has more about this.
In a one sided mattress … there really isn’t any long term benefit to having a soft layer on the bottom and in some cases it could increase the risk of support/alignment issues (depending on the thickness and softness of the layer). It could also affect the durability of the mattress on certain foundations that didn’t provide enough support surface. Unless there was a compelling (or temporary) reason to do otherwise … I would tend to avoid soft layers on the bottom of a one sided mattress.
If you did decide to “stash” a layer on the bottom … I would tend to exchange it for a firmer layer once your best layering arrangement is locked in.
Phoenix