Thanks all, for the lively debate and information on this question. Sounds like a number of opinions out there, and a number of variables to consider.
In this building, the boiler actually can't be turned off, both because the steam loop heats the domestic hot water, and it also supplies another building and is not specific to this building. What I can do is turn off the hot water heating loop through the building.
This would reduce the load on the boiler (I am guessing) and reduce the need to overcool or oversupply the cool air. I assume this would end up with energy savings.
The building cool air comes from pneumatic moduline boxes. The hot water goes to radiators. In buildings down south, we have no problem using moduline boxes, dated though they are, to supply the right amount of cool air with no heat on at all, for six months a year. No humidity problems, and the building in question is in a lower humidity climate. Seeing a hallway with the modulines blowing and radiators on when it is 90 degrees outside in Wisconsin, is why I asked the question. The engineer seemed to think it necessary, and I did not, but since I am on his turf, I hesitate to question him.
I did call a Mechanical Engineer also located in Wisconsin who would have experience with cold climates and boiler heat, and he said no need to have the heat on, but that getting things readjusted would require caution and moving slow. But I also like getting information from hands-on guys as well as designers, so I came here, too.
I will appreciate further advice now that you know a bit more about the setup.