Julie Roberts should choose to mourn her sister's death in which ever way is appropriate for her. No one should say how someone "should" mourn. Show business is her job and sometimes people prefer to stick to the routine that they know during difficult times. Also, we do not know how close she was to her half-sister so even if she took time off to mourn, is it to really mourn or look like a better person in the media? She should mourn (or not mourn) in any way she chooses.
I believe Julia Roberts could continue working, if she chose to. Death and losing loved ones is part of life and something everyone deals with. Whether she needs to take time off for her mourning or not, is not really up to the public or even a question of debate. It's a personal matter that only she can decide on.
No, Julia Roberts should not take time off of show business to mourn her half sister's death, because she can mourn the death while she continues to work. The rest of us do not get to take six months off from work when a loved one dies. Acting can be a good way for her to cope with the loss.
All grieving is different, and every single person should be allowed to mourn in his or her own way. Some take time off to ponder and some decide it is best to keep busy . Julia Roberts should do what helps her to get through this time in the best way.
I would assume the person asking such a question has a limited understanding of human behavior. Everyone handles death differently, and as long as it's not actively harming someone else, it's okay for them to act that way. If she needs to take the time off, she'll do so. It's not up to us.