When I took my CFII ride, we delayed it a day due to IMC. The examiner's comment was that practicing partial panel in IMC is of questionable legality. That sounded reasonable to me at the time. However, over the years I have decided that I no longer agree with him, there's nothing illegal about not looking at certain instruments, which is really all you're doing with partial panel work.
There are really two questions here - practicing partial panel maneuvers in IMC and performing instrument approaches partial panel.
Many times with a student if there are clouds (even if it's VFR, so, say overcast at 3000 maybe) I will request an IFR clearance with a block altitude from ATC - such as "remain with 10 nm of the VOR, 4000 to 7000" and usually I get it if I am flexible on the size of the block. Then we'll go and practice climbs, descents, turns, unusual attitudes, etc. Full or partial panel, doesn't really matter. It's great training.
For an approach, I have not had this exact situation before, but I imagine I would not have a problem performing partial panel approach in IMC with a student who is already reasonably competent and to a ceiling that is reasonably high - say 1000 feet. But CFI workload during any actual instrument approach with a student is dramatically higher than in VMC, so it would depend on a lot of other factors as well.
In the traditional "cover up the AI and DG" version of partial panel, you can use a 3M sticky note and stick it on so that you (the CFI) can see the instrument but the student can't. So that would be a good idea for this situation. For other versions of partial panel (glass cockpit, electric HSI but vacuum AI, or some other variant), it may or may not be more difficult to do this, but each case is different.
What I wouldn't do, though, would be something that takes significant time to un-do. Like, I might turn off the PFD in visual conditions to practice, but I'm not going to turn it off in IMC. That does seem to me to not only be questionable judgment, but questionable legality. If you have a problem, it may take longer to turn the thing back on than you have left.