Yes, it would work, as long as you direct the steam long enough and evenly to each part of the surface. I would make sure that you get the steam outlet into the carboy so you really can reach each part.
Personally, i still would prefer a no rinse sanitiser for ease of use, rather than dicking around with the mop.
Different story if you have one of these baby bottle steam sterilisers, they work perfectly for all small parts like taps and whatever else. Also, some ferementers (the bunnings ones for example) fits perfectly upside down onto one of these, so you can steam sterilise it from the inside.
Thinking about it, you could also fit your steam mop outlet into the carboy and turn it upside down, might be a better solution.
Needless to say that everything needs to be spotless clean before you attempt any kind of sanitation.
Florian