What would happen if 3000 users logged into my site at the same time?

3000 at once would first be a bandwidth issue, then CPU load depending upon what they were all-or-each doing. For example, my chats run on separate servers where ajax chat at the site would definitely cause an overload.

As to multiple logins with one account, I do that at times. However, I would suspect two or more instances of one account editing the same page would quickly frustrate both users as well as possibly getting a complaint either from WordPress or from the server trying to keep up with conflicting database updates (edits/saves).