If I understand you right you'll have an unfinshed(utility room) on one side and a drop ceiling(bedroom/office) on the other of what you are finishing now. If so yes you'll be able to snake the wires through so you can go with a drywall ceiling. Just make sure you won't need access to anything under that area. Because if you put up the drywall and then have to access something the drywall will have to come down. Things to look at are baseboard heat...passageways to third floors..stuff like that.