I have the iphone 6s with a cracked screen and am interested in switching to the SE just because I like having a smaller phone. Would I be able to use my applecare to "downgrade" to the SE?
See this is the kind of thing that has Apple always replacing like for like and never upgrading or downgrading you.
If people got the idea that shortly after a new model was launched they could upgrade or downgrade just how many cracked screens, dropped phones and defective devices do you think Apple would suddenly be dealing with?
So, no. They don't allow this. You get back exactly what you turn in - no more, no less.
Now, if you want to trade in your phone towards purchase of the SE, Apple will be happy to give you a credit towards the SE.