[eluser]Michael Wales[/eluser]
I mean, you could - it would just be a mess. You'd basically use Javascript to alter the href value of the link each time a box was checked/unchecked. Something like domain.com/controller/method/box1,box2,box6,box7. Your method would then have to parse out segment 3 which would contain the boxes that were checked.
So much easier to just submit it as a form - if you need a permalink, based on the forms data, dump it to a database with a unique ID and write a method to return that record.