I think you need to be thinking far further than state management and instead be thinking of the other implications of imposing learning classic asp first.
Rather than learning classic ASP, instead ensure your developers have "state management" as part of their training process. All good training material will include a state management section.
You may run the risk of thinking in the classic ASP paradigm and attempting to apply a defunt design pattern to ASP.net. Instead of making best use of ASP.net's platform and technology.
Having said that I have been developing in ASP.net for a number of years. I am currently maintaining enterprise grade classic ASP systems. Having the knowledge of how the frameworks behind these systems were developed pre-ASP.net is very valuable and HAS improved my ASP.net.
Learning an alternative language is always valuable: Recently I developed an iPhone app in objective-C, it has given me a better understanding of the MVC pattern (the defualt paradigm in XCode) - so will improve my ASP.net in the long run.
Although looking at enterprise systems will be valuable, I do not think just dabbling in classic ASP (i.e. small one-off pages) for the purpose of state management etc is worthwhile and may have detrimental effects. Instead invest time in learning ASP.net "well" (i.e. include state management).
n.b. I have found it tricky not to turn this into a classic ASP / ASP.net debate. Instead tried to concentrate on the learning.