Nah. Would make grinding too easy. Plus you would need to run the same deck in both anyway.
But it would be great!
You could achieve high elo scores while winning dms and dts and getting 30+ survivor at once!
In a perfect world
I'm not an expert on the matter, but I really doubt you can do all that with one deck even if you played them separately.
Which in turn would clash with the current scripting that only allows one deck at a time.
Next you'll argue that they should create the possibility of saving multiple decks at once to different game rooms.
Right now, since you can only play in one room there just isn't a reason to keep that many 'active decks'. And you can save the presets already and the dropdown menu is right there with the game client. That's as fast way to change between decks as you need unless they for some weird reason do follow through on your idea.
I know enough that it would mean more work for the staff.
Also, how would you deal with say, someone owning only one Flanagan and wanting to use it two decks?