My school has a letter service (people send them in to the pre-med office and then they copy and send them out in a packet to all the schools you designate). Some schools said absolutely not to send more than X number of letters, but they sent out all 6 anyway and it didn't hurt me a bit.
If someone else is sending them all, it is all right, but if you were having people send them individually, it might seem like you weren't paying attention.