Yes this is possible. For an FDM/FFF printer, you'll need to print with supports. I might also recommend printing in PLA to minimize the chance of warping during the print (from experience).
It might also help to slow down the feedrate to ensure smooth surface finish and avoiding delamination on such small layers.
You'll probably see a decrease in the surface quality on the inside due to the printing of support scaffolding depending on the slicing engine you use.
You'll want to pay attention to the strength of the case. If you print the case upright then it will be more susceptible to breaking without post-processing.