I cried more than once during my first placement. Mostly just infront of my practice teacher, but on one occasion a couple of other staff members were around.
During the same placement an OT started crying in the office one day because of the sheer amount of work she had to get through basically, and the other staff were very supportive, offering to listen if she wanted to talk/making her a cup of tea etc.
Obviously crying every day, at everything, isn't very professional, and probably suggests you need help/support beyond the workplace. But when it is occasional/caused by extreme situations etc, I don't think there is anything wrong with it as long as it is confined to the office and not infront of service users. Social work is a very stressful job and if less of us tried to bottle everything up rather than letting it out sometimes, it will probably help everyone.