I can function in the sense of working and doing other busy activities in spite of feelings, and I can usually even hide these feelings if I need to, but I do not detach from feelings to do the thinking/acting bit, i.e., to "work" in our cultural idiom. Threes require detachment from the Heart Center in order to think and act effectively; the idea of feeling is uncomfortable for Threes who are trying to function.
Even if Threes are not depressed or faced with the danger of emotion at the level of crisis, they will still require this detachment from their Heart Center in order to use the amalgam of their Head and Gut Centers. They fear that if they allow themselves to go into feeling mode to any extent when they're working, the feeling will incapacitate them. They might be able to dramatize emotions when they're working, but they cannot let themselves engage in emotional feeling and work at the same time.
As a Four, if I'm overwhelmed by a feeling, which is rare (my Tritype and instinctual stack, in addition to my wing, make me less depressive and more resilient than many Fours have described themselves as being), I need to work through the feeling before I'm functional again. If I'm bothered but not quite thrown into crisis by a feeling, I may be able to conceal this disturbance and function anyway, but the feeling stays with me, often in the forefront of my mind.
In short, I cannot detach from feelings as Threes do. I can either stop working, suffer a decrease in the ability to work, or hide the feeling and work anyway. Threes, on the other hand, not only can detach but must detach in order to work.