No, not at all. If you are JUST running Missions and are not interested in joining the Demo Team (at this time, maybe later) and you don't foresee your players taking their characters to other 'Missions Legal' tables, then you don't need any sort of 'account' number.
In fact if the above is true, you don't need documentation at all, except for your own use.
If you foresee your players going to another 'Missions Legal' table with their character, then they will want those logs... maybe. I don't see any Missions GM kicking someone off the table with an otherwise Missions Legal character simply because they can't produce all of their logs.
In either case, you can't be a 'Missions Legal' character if you run them through anything outside of the Missions line and they keep their Karma and rewards. You CAN run them through a non-Missions line adventure and they can stay Missions Legal as long as they don't keep any Karma/Nuyen/Street Cred/ Contacts, etc.
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Now, if you want to become a CDT Agent, this sort of changes. As a CDT Agent, anytime you run an OPEN table event (that is at a Public Venue registered with Catalyst and that is open to the public, so anyone can sit down) you will earn a credit if you report the event, how many people attended, who they were, etc. You can use those credits to get PDF copies of Shadowrun source material and fluff.
Currently, players can also be marked for attendance but there is no benefit to do so... though Catalyst is trying to think of something.
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Anyway, bottom line, if this is just you and a group of friends, there is nothing more that you need to do than get a copy of the adventures and run them.