Doable? Yes. It will take much longer to get the cross country time though. It's been a while since I last instructed but I recall the instrument students providing the most cross country time. There is no requirement that the flying be done during the day, so it's easy to get night time with instrument students as well.
Where I instructed, fog would often shut down operations for days on end during the winter. Some of the instructors that didn't have the II were canceling all of their lessons. I'd take off with the student IFR, fly up into the foothills for the lesson and pick up an IFR clearance on the way back. I suppose they could have just flown it themselves but I think they were IFR non current too.
I preferred doing instrument training, it provides more consistency in your schedule, since all of the student's flights are dual.