Fondant mats are fun, and I have used them a ton on cakes and mousse, just not on soap (Yet! Seriously, I need to do this too, soon!)
If you remove the M&P from the mat, cut it into shape and stick the M&P to the bottom of your soapmold, the heat from the soap may ruin your pattern made from the mat, and melt or wobble it. If you use a mat, the pattern will stay as is, as the mat will support the pattern all the way even when the soap heats up.
However, if you stick the soap in the freezer to prevent gel/ heating of the soap it may work this way!
You could also make the M&P to make an imprint of the mat. Then just cut out a strip that fits the mold perfectly and put the M&P lace on top of your finished soap, as a 'roof'. That will give you a perfectly finished top on your soap.
Just make sure you put the lace top on when your soap is stiff enough to support it and not sink, but not so stiff it will not stick to the batter. Then gently press it onto the batter with a flat surface so you get no airpockets under it. Then simply let it sit until ready to cut/unmold.
But again, doing it either way - without a mat - you can not gel your soap, or the M&P will surely wobble/melt or whatnot, and ruin the pattern you worked to obtain.
Hope that helped, and good luck! : -)