the answer to your question is yes, precast can be used as a diaphragm. Usually precast (is this precast only or prestressed, like double tees or hollowcore?), has standard design details like dowels that tie it into shear walls. The precast is set into place and the ends are grouted such that the dowels are connected to the precast. Sometimes, you need to apply a lightly reinforced topping to get the shear loads transfered or attach the panels to each other with weld plates. You need to get the PCI Design Handbook for some examples. Most standard precast has allowable shear loads. Or you can post them on your drawings and let the precaster's engineer design for them.
You do confuse me with your statement about columns. Precast is more likely to be used with a bearing wall/shear wall system. A column system would have concentrated shears at the columns which would be difficult to transfer with dowels or other standard details.