I have this boot liner in my Panda & it does not make any difference in terms of sound deadening, I have found though that since owning my Panda the one part that does make a difference is the rear parcel shelf as when this is not fitted I get a slight whistling sound from the rear but when the shelf is put back in the sound goes, one of the many quirks of Panda ownership
Short answer: no. It is quite thin, flexible plastic, similar (but thicker) to what plastic milk bottles are made from.
Most of the noise from the rear comes via the air exit vent in the vertical face of the boot, behind the bumper (which is why @FiatMatt94 hears a whistle with the shelf out), or from the wheel arches, part of which is where the upright part of the rear seat meets the bit you sit on just inside the car (and which is much more noticeable with the seat folded of course).
The moulded tray is brilliant though when putting wet or muddy things in the boot (I’m a river monitor and conservation volunteer, and often have wet boots, nets, etc — or, in coppicing season, a lot of firewood! — in the boot). It can hold quite a volume of water and stops that reaching the seats or the spare wheel well.