It causes the vinyl to be gummy - Thats the main, irrefutable one that everyone who installs will notice. Why does the vinyl become gummy? Because a solvent is a certain percent of alcohol, alcohol that needs to evaporate. When you overlam it right away... where does that solvent go? It usually stays and goes out the back, where the glue is. And as you know... glue doesn't like alcohol.
Will it cause a problem? 9/10 times, no. We used to laminate right away quite a bit - We had a few failures... Not one or two, but a few. Ones where we had to waste a lot of time to go, inspect the sign.. see it wasn't anything the customer did, remove the sign.. reproduce it, and put it back up. So when we had a solvent, we waited 8-12 hours before laminating... Unless it was a rush job, then we waited as long as possible and stopped.
What could happen from laminating right away?
The glue becomes gummy... which makes installing harder, which makes it prone to more installer mistakers / redos.
The solvent goes somewhere... Either it goes up and the overlaminate bubbles, or it goes back to the glue and increases the chance of glue failing.
Your warranty is void - Does it matter? How often do you submit warranty when it comes to material? 3M at least will take the material back and run tests on it... and I'm sure they can tell if it was properly offgassed. But as I said... how often do you do warranties? doesn't really matter.
What will happen from laminating right away? 99/100 times... nothing. But that 1 time could be a $10,000 job that you just threw down the drain. Rule of thumb is if you can wait, then wait... If it's a complete rush job, it's a small risk. If you find yourself in a situation where you can't wait more often than not... Invest in a printer that doesn't need offgassing, such as Latex or UV, depending on your application. Or go with one that requires very little offgassing like the new Epson.
In a pinch you can use a heatgun and heat it up... it'll help disolve all the solvents. Not useful for a big job... but hopefully you're not rushing big jobs!