Can I nail mass loaded vynl onto plywood?
Obviously, the wall can’t be made to be floppy; but the soundproofing inside the wall can be floppy.  In the Science of Acoustics, we call it a “Limp Mass Barrier.”  This is typically why the Mass Loaded Vinyl is instructed to be installed against the studs and then drywall over it. This allows the barrier to move in 3-Dimensional space and bleed off the energy of the sound, resulting in greater net losses of sound propagation through the wall.
“But I don’t want to rip down my sheet rock to put this stuff up.”  That’s fine, no need to really.  The solution here is to find the studs behind the existing sheetrock with a stud finder, mark them with a blue line, and screw in some Furring strips vertically-through the sheetrock – into the studs.
– acousticalsolutions.com

Stick with nails if that's what you got. No glue if it's temporary. I'd probably use exterior screws.
It's supposed to be furred out so that at least one side can move freely. Then you could even sandwich the furring strips with two layers of vinyl and then plywood it.