16 marines?
Without micro, a BC kills 11 marines (with 12 marines, 2 survive).
That's even less with either stim or shield.
It isn't logical that you have upgrades when you're going for BC rush (unless you want to wait a while, and you will have at most +1 atk or def, not both - while marines can have +1/+1 already and maybe even both stim and shield).
Then again: it is silly to go for a frontal assault against BC's.
With micro, any number of vikings can kill a BC without a single viking getting killed (superior range + speed).
I guess it is good against an unprepared opponent, but once he gets vikings out (and can do a minimum of micro), he will destroy the BC.
HOWEVER, a BC has the advantage of being repairable, so a BC semi all-in would be pretty sweet I think.
And I just do not like slow units. It's not the way I play the game, no matter how 'strong' it may be (just like I won't use the brood lord-infestor combo easily).