I know this is two pages old at the point, but just got caught up with where I last read. Liquid Nails does dry super hard and thats the problem with using it as a sealant. Boxes flex. When they do and you have a super hard unforgiving "sealant" (adhesive) then you run the risk of cracking the sealant and not being sealed anymore. As compared to other sealants, say latex for example. They are made to remain slightly soft and flexible, so that when whatever they are sealing moves a little bit, it stays sealed over time.
Short description:
Latex caulk = long term sealant
Liquid Nails = long term (and insanely strong) bonding material
use good caulk for sealing seams, luquid nails for layering sheets of lumber, or glueing cats to walls....