I would look online at some of the Dynamat or alternative sites to see how the stuff works. If all you are doing is insulating then the pond liner has some merit, but the self stick deadners actually dampen the vibrations in the metal. In order to do that they have to be mechanically attached to the entire surface of the metal. I guess if you spread the liquid nails evenly over the surface, the pond liner could work in the same way.
If you are just trying to seal the door with a thicker plastic, it would work as well.
One low budget alternative in low temperature climates is to use Ice and Water Shield from the hardware store. It is a bitumous sticky black sheet that is used in roofing to replace the tar paper in certain applications. Our hardware store sells it in 12" rolls to flash windows in new construction. as well as the industrial 36" rolls. That stuff also sticks to the metal and the asphalt in the bitumous compound dampens the sound vibrations. I thought about using this stuff because I just am just finishing my house and I have some left over so $=0. I decided not to for two reasons. #1 For a time it outgasses and smells like a new road. #2 ,more importantly, reportedly around 180 F it melts and I didn't want a puddle in my door and everywhere else in my cab. I live in the desert southwest and car interior do get that hot. The stuff I went with is from Phoenix, AZ and is rated to ~ 500F.
I think I may use some of the free stuff I have in my shop on the insides of the fenders and under the hood to reduce engine noise. If it melts there, no biggie.
If you go with the pond liner though, I would be interested in hearing reports on how well the sound deadening aspect works.
Ken