You need to use a letter service that will hold the letters for you till AADSAS opens up. If the letter touches your hand theoretically it has lost all confidentiality and is almost worthless at that point. At my school the pre professional office had a letter service and the professors sent them there directly. Once AADSAS opened up I paid my $15 or so and they were mailed off.
There is the option for your professors to upload it directly to AADSAS but honestly I didn't trust their computer skills, plus it was extra work as they had to log in and create an account.