Of course. Any reasonable employer is going to understand that an unproductive worker isn't good to have around the office. If I'm not going to be productive because something else is occupying my attention, why pay me to come in and do nothing? Better I take one of my limited sick days, which the employer is already paying me for, and take the time to get my head right.
I never feel guilty for taking a sick day for that. I feel guilty when I use a sick day because I've over-indulged the night before and am fighting off a hangover. That's a stupid reason to use a sick day since it belies a lack of personal responsibility.