It can definitely be done if you write a Custom Class (in other words, Java). But I don't know of anyone who has done it before so you'll be blazing some new territory.
The first step would be pulling down the Vassal source code and get it compiling on your computer -- see the Wiki for some articles on getting "git" set up (so you can pull down the source code), and then I think there's stuff about how to get your development environment set up (I think we're currently recommending IntelliJ if you don't already have a favorite).
Then you'd need to learn how to override VASSAL classes with your own custom classes. There's a "Coding Tutorial" in there somewhere (and ZapWars in the module section is related to that) which attempts to walk you some of the basics. You'd be looking for some good place to override a Vassal class with your own, so that you'd have an insertion point for you code. The code would have full access to the game state data by calling into Vassal methods, and could then write out whatever you want to a file (and/or read it in from a file). I guess the Deck trait even already has a thing to read/write hands of cards to and from text files, so you could take a peek in there.
I'm not saying it's easy, but it's possible if you've got some Java chops

Brian