I applied for summer internship(BSc level) in applied math in one of the North European countries a month ago. I would consider myself as a good applicant but I suspect that they accept very few international candidates, and range of countries of applicants is pretty wide. It is stated that the time of selection decision is march-april. I'm very curious and impatient about knowing the answers to "am I accepted or not?", "when will I get the answer?". In addition to curiosity, the reason of sending such email is to show that I'm ambitious(?) and serious and didn't applied just for fun. I believe that this might increase a little bit my chances. But I'm afraid that this email might turn against me, because I disturb the committee for almost(?) no reason, and it might give them an image of impatient student.
I would not suggest to write an email that does only ask for the status of the application before the announced time of selection is over—even when the email is totally calm and polite. The program has a schedule, the applicants are supposed to know the schedule.
However, you may have some other good reason to write an email. As Thomas commented to another answer: A good reason to ask for the status would be an offer for another opportunity. You could also try to find another good question to ask (but be sure that it is not already answered in the FAQ or wherever). Also, you could provide some new relevant information, if there is any (e.g. some new grades, completed projects,…).
Sending a simple email politely asking about the status of the applications should neither hurt nor hamper your chances of acceptance. Anything more and you risk annoying the committee and hurting your chances.