[someelephant]

If you throw out a time complexity most interviewers will tell you if they expect something better. For big companies, it's always a crap shoot. For smaller companies, if the person isn't willing to have a conversation with you it's a sign they would be difficult to work with.

[titanomachy]

Not just throwing out a time complexity to see what sticks, but if you sketch out an approach and give the complexity then I agree, they will probably either tell you “implement that approach” or ask “can we do better?”.