Once I have uploaded my library to match, can I delete local files?

My music is backed up on a couple of external hard drives, I know I can use iTunes match to upload all of these to the cloud and then play them from authorised devices. Does it matter if I then disconnect the external hard drives and no longer have any local files in my iTunes library? I know that iTunes match auto updates any changes to your library so would it remove all my files from the cloud once it sees they are removed from my iTunes library or can I safely disconnect my external hard drives?