Yes, home inspectors do look in closets. Often times closets can have an attic access, drainage or supply pipes that run behind drywall or duct work. Failing to look in a closet can be detrimental to a home inspection due to the fact there could be countless amount of defects within the closet.
Sometimes people like to hide a fuse box with shelving or other décor, but inspectors need to take the cover off to take a look inside.
If you reach your attic through a closet, move any clothing or stored items out of the way. The same goes for hatches for crawl spaces.
Granting easy access means fewer delays and less time on the market. If an inspector can’t examine places that you’re supposed to report on, time that could be spent negotiating with buyers gets eaten up by arranging for another inspection appointment.