It's not generally done in missions, because for a large number of Agents having to go through and pay close attention to every bit of a fic would drive them round the bend (unless it's a very short fic). If you want to snark at everything, you'd probably be better off writing an MST. Which is great fun, especially if you partner up with someone else to do it. :D

When you snark every line of dialogue, you've written an MST. Personally, I don't consider those missions, because there usually doesn't happen anything else than the snark. There's usually not much of a story. I guess it would be possible to have mission things happen, such as writing down charges, admiring the scenery (or commenting the lack thereof), getting on each other's nerve, i.e. have a story and still snark every line of dialogue.

For a mission you need permission, for an MST you don't. There are no rules concerning how you write a mission, other than the rules that apply to writing fanfic. That means you are allowed to write a mission where you snark every line of dialogue. Though I don't really see why you would want to.