Are you talking about the internail mail box? If so that's different from the one on the 2nd floor (which has slots for ticket refunds, medical claims, education claims etc)
If you dropped it in the internal mail you'd need to be sure it's addressed to the correct dept (or make sure you have a copy so when it invariably doesn't arrive you can send it again)
Imho it's worth the quick walk upstairs to put it at the 2nd floor as the couple of times I've sent via internal mail it 'never arrived maam'