Today's stay open inks which seem to be very much in vogue, really never do reach the point of "dry", even when some jobs are bound and sent from the printing plant to the print customer. The ink's mechanism relies on the "set" properties, which is the first phase of a three step process. Being set, a job that has been aqueous coated allows continuance of the oxidative process while the journey continues to complete polymerization evolves. Aqueous coating does not shut off the ink films underneath from the needed oxygen. It weaves it through a honeycomb layer of coating to complete the process.
As far as printing with aqueous coating and post lamination, it is quite beneficial to print with a size type aq coating to promote better laminate adhesion versus a non coated print job. The importance is to work closely with your suppliers and develop a trusting, experienced relationship so the results you expect are the results you get.
Not to stray from the subject, but I will add this. Inks that are formulated to "dry" in favor of the importance of setting are much more likely to succeed over time and the gamut of jobs that go through a normal commercial offset press room. All it takes is one bad apple of a poorly dried job to wreak havoc and possibly cause a bad ripple effect within your company. Food for thought.
D Ink Man