I tried that with cardstock in my other lacy card thread. It doesn’t help with charring there, by which I mean the actual burning away of small bits of edges because the laser lingered too long, but it cuts down on smoke staining. However, in this case there is almost no overburning and very little smoke.
This particular design is too fragile for masking paper with paper, and it wouldn’t help with the soot, which is spread by handling. Stacking multiple sheets would just result in double the confetti.