You'll never be able to do anything but vibrato on the high e with those kind of strings without it breaking if you can even tune it that high to begin with, but that's fine if that's that's your thing.
You might find that the really heavy bass strings might not be able to entirely fit into the nut, but that shouldn't be much of an issue because at the very worst the string will be nice and snug and the action will be higher there (but still easily playable, talking from experience), and at the best the nut will quickly 'stretch' to accommodate the string. (Talking about traditional nuts here, I have no idea about locking and metal nuts, which might be more of issue).
You might find that the really heavy bass strings might not be able to entirely fit into the nut, but that shouldn't be much of an issue because at the very worst the string will be nice and snug and the action will be higher there (but still easily playable, talking from experience), and at the best the nut will quickly 'stretch' to accommodate the string. (Talking about traditional nuts here, I have no idea about locking and metal nuts, which might be more of issue).
