Yes. Especially in Computer Science because you will need to fit into a group at the University you are applying to, so it is useful to know before if the professor will have space in his/her research group for new students. It doesn't work this way in other fields, from what I've seen, but in Computer Science you need a prof to be willing to have you in their group. I met with a prof last month who told me that I should let him know when I have applied, so he can look out for my application because there was an applicant a couple years ago that wanted to work with him and he didn't realize that that person had applied. The applicant didn't get in simply because he didn't notice her application in the hundreds that they receive and so her application 'slipped through the cracks'.
I wouldn't recommend this. Sometimes profs put on their websites that they don't have the time to respond to individual emails - did you check this prof's website? If they don't reply I would suggest contacting another prof who you're interested in at that school, or even try contacting the prof's grad students. If they don't reply and you still want to apply to that school, make sure that you mention that prof in your SOP and how you would fit in with their research. You might want to consider sending an email when you apply too, so that they can look out for your application (although I'm not sure of the etiquette here if you've never contacted him/her before)